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Graduate Theses, Dissertations, and Problem Reports

2001

Design and analysis of a hybrid steel/composite pipe for high-Design and analysis of a hybrid steel/composite pipe for high-

pressure applications pressure applications

William Jennings Briers III West Virginia University

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Design and Analysis of a Hybrid Steel/Composite Pipe for High-Pressure Applications

William Jennings Briers III

Thesis submitted to the College of Engineering and Mineral Resources

at West Virginia University in partial fulfillment of the requirements

for the degree of

Master of Science in

Mechanical Engineering

Ever Barbero, Ph.D., Chair Victor Mucino, Ph.D.

Gregory Thompson, Ph.D.

Department of Mechanical and Aerospace Engineering

Morgantown, West Virginia 2001

Keywords: Autofrettage, Composite, Hybrid, Pipe, High-Pressure, Torque

ABSTRACT

Design and Analysis of a Hybrid Steel/Composite Pipe for High-Pressure Applications

William Jennings Briers III

Once limited almost exclusively to aerospace applications, the use of composite materials has become widespread among many high performance industries. Today’s petroleum industry is requiring piping systems to sustain high pressures, impact, rugged handling, and harsh environmental conditions such as corrosion and temperature. Advances in the last decade of engineered materials have opened the way for more conversions from metal to composites.

The objective of this research is to develop a lightweight composite pipe that meets the performance requirements of an existing high-pressure steel pipe. This development is crucial to the petroleum industry where hydraulic-fracturing services are demanding lighter weight materials while maintaining low cost and high reliability. A hybrid steel/composite pipe was designed and analyzed using the finite element analysis (FEA) programs SDRC® I-DEAS® and ABAQUS®. The design consisted of a thin-walled steel liner with a composite over-wrap. It employed the use of unique end fittings, which transfer longitudinal and torque loads from the steel to the composite. This research is believed to be the first instance where autofrettage is used on a metal lined composite pipe. Results from FEA were used to validate the design and fabricate a full-scale prototype. The prototype was successfully tested and exceeded maximum design pressure.

iii

Dedication

This document is dedicated to my father, William Jennings Briers Jr., who

through a difficult battle with cancer did not survive to see this accomplishment. His

expertise in engineering and wisdom in life was a tremendous source of encouragement

and strength for me. He was a person with great character and integrity, an engineer with

impeccable ethics, and most importantly a man with complete love for and faith in Jesus

Christ.

iv

Acknowledgments

I thank God, above all, for giving me the strength and ability to accomplish this

goal.

I would like to express great appreciation to Dr. Ever J. Barbero, my advisor, for

his guidance throughout my studies at West Virginia University. His knowledge and

experience was of tremendous value to this project and has helped to prepare me for a

career in engineering.

I would like to thank Halliburton Company for funding this project. Especially, I

am grateful to Stan Stephenson for overseeing my research and providing valuable

insight based on his years of field experience.

I am very thankful for the assistance of my sister Becki Briers Booras, and my

friend Ed Wen. I appreciate their support and helpful advice throughout this research.

I would also like to acknowledge my roommates, Andy Manzo and Eric Liese, for

their understanding and patience during the conclusion of my writing. They were very

kind for doing my share of the dishes.

I am especially grateful for the love and support of my mother, Sue Briers. I

appreciate her constant encouragement and unfailing confidence in me.

v

Table of Contents

Title Page i

Abstract ii

Dedication iii

Acknowledgements iv

Table of Contents v

List of Tables vii

List of Figures x

Nomenclature xiv

Chapter One: Introduction and Literature Review 1

1.1 Introduction 1

1.2 Literature Review 4

1.2.1 Composite Materials 4

1.2.2 Autofrettage 5

1.2.3 Hybrid Composite Structure 8

Chapter Two: Initial Design and Analysis 11

2.1 Steel Axisymmetric Model 11

2.2 Composite Material Selection and Bi-Directional Laminate Design 13

2.3 Three-Directional Laminate Design 22

2.4 Hybrid Steel/Composite Axisymmetric Model 23

2.5 Optimization of Hybrid Design 28

2.6 Bending Analysis 31

vi

2.7 Conclusions 35

Chapter Three: Development and Analysis 53

3.1 Hump Design for Longitudinal Stress 53

3.2 Material Substitutions 56

3.3 Analysis of the Sleeve Design 57

3.4 Ovalization Analysis 59

3.5 Track Design for Torsion Load 61

3.6 Simplified Torque Analysis 63

3.7 Finite Element Analysis of the Track Design 65

3.8 Conclusions 67

Chapter Four: Fabrication and Testing 96

4.1 Fabrication 96

4.2 Testing 98

Chapter Five: Design Modification 102

Chapter Six: Conclusions and Recommendations 111

6.1 Conclusions 111

6.2 Recommendations 112

References 115

Appendix A – Instructions for Modification and Analysis of the Hybrid 117

Steel/Composite Pipe Using SDRC® I-DEAS® and ABAQUS®

Appendix B – ABAQUS® Input File (hybrid1.inp) 151

vii

List of Tables

Chapter 2

2.2.1 – Orthotropic elastic material properties of AS4 in unidirectional and 37 ±±±±20°°°° bi-directional lay-ups. 2.2.2 – Required composite thickness to autofrettage 0.155 inch thick steel 37 according to bi-directional fiber orientation ±θθθθ. 2.3.1 – Relation between orthotropic elastic material properties in the

ABAQUS® 38 coordinate system and the coordinate system used for calculations in

Microsoft® Excel. 2.3.2 – Initial tri-directional hybrid design describing composite and steel 38 thickness and equivalent orthotropic elastic material properties using

AS4 composite in a [±±±±20°°°°,90°°°°] lay-up. 2.3.3 – First Ply Failure and Fiber Failure values for the initial tri- 39 directional hybrid design using AS4 composite in a [±±±±20°°°°,90°°°°] lay-up. 2.4.1 – Description of limiting stresses and symbols for the steel and 39 composite. 2.4.2 – Finite element analysis results for the initial tri-directional hybrid 39 design incorporating hoop thickness from flawed equation. 2.4.3 – Finite element analysis results for the initial tri-directional hybrid 40 design incorporating hoop thickness from corrected equation. 2.5.1 – Optimized tri-directional hybrid design describing composite and 40 steel thickness and equivalent orthotropic elastic material properties

for AS4 composite in a [±±±±20°°°°,90°°°°] lay-up. 2.5.2 – First Ply Failure and Fiber Failure values for the optimized tri- 41 directional hybrid design using AS4 composite in a [±±±±20°°°°,90°°°°] lay-up. 2.5.3 – Finite element analysis results for the optimized tri-directional 41 hybrid design. Chapter 3

3.2.1 – Known properties of TR50 carbon fiber and EPON 828 epoxy. 70

viii

3.2.2 – Properties used in CADEC© to determine transversely isotropic 70 material properties for a unidirectional composite of TR50/EPON

828. 3.2.3 – Transversely isotropic elastic material properties for a unidirectional 71 composite of TR50/EPON 828 produced in CADEC©. 3.3.1 – Sleeve design describing composite thickness, liner thickness and 71 equivalent orthotropic elastic material properties for TR50 composite

in a [±±±±20°°°°,90°°°°] lay-up. 3.3.2 – First Ply Failure and Fiber Failure values for the sleeve design using 72 TR50 composite in a [±±±±20°°°°,90°°°°] lay-up. 3.3.3 – Finite element analysis results in steel and composite along the section 72 of constant thickness, away from the hump/fitting. 3.3.4 – Equivalent orthotropic elastic material properties for TR50 composite 72 in a [90°°°°] lay-up. 3.3.5 – Maximum stress values from the FEM of the sleeve with 73 reinforcement. 3.3.6 – Sensitivity FEA results from the section of constant thickness using 74 114 ksi yield strength steel. 3.3.7 – Sensitivity FEA results from the section of constant thickness using 74 126 ksi yield strength steel. 3.4.1 – Results from ovalization analysis showing the maximum stresses and 75 safety factors at fiber failure for the steel and the three groups of

composite elements. 3.6.1 – Values of FFshear, FFF and ννννh for the simplified torque analysis. 75 3.7.1 – Results from the torque analysis describing the maximum shear 75 stresses, fiber failure values and safety factors for the [±±±±20°°°°,90°°°°] base

composite and the [±±±±20°°°°] composite in the tracks. Chapter 4

4.1 – Individual component and combined weights of the hybrid pipe. 100 Chapter 5

5.1 – Fiber properties of TR50 and Kevlar® 49. 105

ix

5.2 – Orthotropic elastic material properties of TR50 and Kevlar® 49 in 105 separate unidirectional lay-ups. 5.3 – Modified design describing composite thickness, liner thickness and 105 equivalent orthotropic elastic material properties for TR50 and

Kevlar® 49 in a [±±±±20°°°°,90°°°°] lay-up. 5.4 – FEA results for the constant thickness section of the TR50/Kevlar® 106 design. 5.5 – Maximum stresses and factors of safety from the finite element 107 analysis of the TR50/Kevlar® design. 5.6 – Modified design of TR50 and Kevlar® 49 in a [±±±±20°°°°,90°°°°] lay-up with a 108 10% increase in base composite thickness. 5.7 – FEA results for the constant thickness section of the TR50/Kevlar® 108 design with a 10% increase in base composite thickness. 5.8 – Maximum stresses and factors of safety from the TR50/Kevlar® 109 design with a 10% increase in base composite thickness.

x

List of Figures

Chapter 2

2.0.1 - Original pipe with hammer union fittings and wingnut. 42 2.0.2 – Stress resultant versus strain graph for the autofrettage process in the 43 hoop direction. 2.1.1 - Steel axisymmetric model. 44 2.1.2 – FEM with boundary conditions. 44 2.2.1 – Thickness versus lay-up angle for a bi-directional laminate. 45 2.2.2 – Weight per length versus lay-up angle for a bi-directional laminate. 45 2.3.1 – Material coordinate systems for Microsoft® Excel and ABAQUS®. 46 2.3.2 – AS4 lay-up as defined in CADEC©. 46 2.4.1 - Hybrid axisymmetric model. 47 2.4.2 – FEM of hybrid pipe. 47 2.4.3 – FEM of hybrid pipe showing detail of gap elements and Coupled 48 DOF. 2.5.1 – Four case comparison of steel thickness versus composite hoop 49 thickness. 2.5.2 – Four case comparison of steel thickness versus weight of the steel and 49 hoop wound composite. 2.5.3 – Four case comparison of steel thickness versus safety factor for the 50 hoop wound fibers at autofrettage pressure. 2.5.4 – Four case comparison of steel thickness versus modified safety factor 50 for the hoop wound fibers at autofrettage pressure. 2.6.1 – Pipe supported at midpoint for first beam bending scenario. 51 2.6.2 – Shear distribution for first beam bending scenario. 51 2.6.3 – Pipe and boundary conditions for second beam bending scenario. 51

xi

2.6.4 – Shear distribution for second beam bending scenario. 51 2.6.5 – Pipe and boundary conditions for third beam bending scenario. 52 2.6.6 – Shear distribution for third beam bending scenario. 52 Chapter 3

3.1.1 – Initial hump design for longitudinal stress. 76 3.1.2 – FEM of initial hump design showing detail of gap elements on lower 76 hump. 3.1.3 – Stress contour for initial hump design showing massive elongation 76 and intersection of steel and composite. 3.1.4 – Meshed hump section showing detail of gap elements aligned normal 77 to the spline curve of the hump. 3.1.5 – Sleeve design without composite over-wrap. 77 3.3.1 – Two case comparison of steel thickness versus modified safety factor 78 for the hoop wound fibers at autofrettage pressure. 3.3.2 – Two case comparison of steel thickness versus weight of the steel and 78 hoop wound composite. 3.3.3 – Exploded view of sleeve model showing the three parts. 79 3.3.4 – Meshed finite element model of the sleeve design. 79 3.3.5 – Exploded view of sleeve model with reinforcement over the humps. 80 3.3.6 – Diametric dimensions of the hump/fitting for the sleeve design. 81 3.3.7 – Thickness dimensions of the hump/fitting for the sleeve design. 81 3.3.8 – Longitudinal dimensions of the hump/fitting for the sleeve design. 81 3.3.9 – Angular dimensions of the hump/fitting for the sleeve design. 82 3.3.10 – Radial dimensions of the hump/fitting for the sleeve design. 82 3.4.1 – Cross-sectional and three-dimensional views of the model used for the 83 ovalization analysis.

xii

3.4.2 – Three-dimensional view of the model with shaded area describing 84 load location. 3.4.3 – Cross-sectional view of the model with arrows depicting seven rows 85 of nodal forces. 3.4.4 – Cross-sectional and three-dimensional views of composite elements 86 from which results were taken. 3.5.1 – Unwrapped view of the large hump showing dimensions of the track 87 design. 3.5.2 – Dimensions of the track design in a cross-sectional view. 87 3.5.3 – Variable dimensions used to determine the track design. 88 3.5.4 – Diagram used to determine the radius of the track bottom at the 88 bottleneck of the track design. 3.7.1 – Longitudinal cross-section of steel hump section without large hump. 89 3.7.2 – Solid model of steel hump section without large hump. 89 3.7.3 – Solid model of the four steel diamond shaped track forms. 90 3.7.4 – Solid model of the completed steel hump section with tracks. 91 3.7.5 – Meshed FEM of the steel hump section with tracks. 91 3.7.6 – Longitudinal cross-section of composite section including 92 reinforcement. 3.7.7 – Solid model of composite section including reinforcement. 92 3.7.8 – Interior view of the composite showing diamond shaped cutouts. 93 3.7.9 – Meshed FEM of the composite part. 93 3.7.10 – End of steel mesh showing node, rigid bar elements and applied 94 torque load. 3.7.11 – Steel part of the simplified model for the torque analysis. 95

xiii

Chapter 4

4.1 – Hump/tracks showing ±20ºcarbon fibers and the triangular shaped 101 void. Chapter 5

5.1 – Exploded view of the sleeve model with base and reinforcement 110 composites modeled as a single part. Chapter 6

6.2.1 – Possible design of raised guides for aiding fiber alignment upon 114 exiting the tracks into the turnaround area.

xiv

Nomenclature

English

Symbol Description Unit

a Arc-length in A Area in2 c Center in C Stiffness Matrix - d Inner Diameter in E Modulus psi F Force lbf FF Fiber Failure Stress psi FPF First Ply Failure Stress psi g Gravitational Constant ft/s2

G Shear Modulus psi I Moment of Inertia in4 J Polar Moment of Inertia in4

l Transformation cosine or length -, in m Transformation cosine or mass -,lbm M Moment in-lbf n Transformation cosine - N Stress resultant or number of tracks lbf/in p Pressure psi r Radius in R Reaction Force lbf S Compliance Matrix - S.F. Safety Factor - t Thickness in T Torque in-lbf U Strain Energy in-lbf v Velocity in/s V Percent Volume Fraction % w Weight Per Length lbf/in W Weight lbf Greek


ε Strain µin/in ∆ Change in - ν Poisson’s Ratio - ρ Density lbf/in3

σ Stress psi

xv

Greek (cont.)


τ Shear Stress psi θ Angle degrees

Subscript

Symbol Description

1 in the Fiber Direction 2 in the Transverse to Fiber Direction 3 in the Through Thickness Direction 12, 21 In-Plane 13, 31 Inter-Laminar Plane 23, 32 Inter-Laminar Plane c of the Composite c2 of the Composite f of the Fiber fail at Failure fitting of the Fitting FPF at First Ply Failure FF at Fiber Failure h, hoop Hoop Composite or Direction H of the Hammer limit Limiting Factor long Longitudinal Composite or Direction m of the Matrix/Resin max Maximum Value p of the Pipe Q at Autofrettage Pressure Qc of the Composite at Autofrettage Pressure Rc of the Composite Post-Autofrettage Rs of the Steel Post-Autofrettage s of the Steel shear Shear Value track of the Track Von Mises Calculated using Von Mises Wing of the Wing-Nut Yield at Yield Stress of the Steel x in the Global x Direction y in the Global y Direction z in the Global z Direction xy, yx in the Global xy Plane

xvi

Subscript (cont.)

Symbol Description

xz, zx in the Global xz Plane yz, zy in the Global yz Plane Superscript

Symbol Description

-1 Matrix Inverse T Matrix Transpose θ of the Angle θ

1

Chapter One

Introduction and Literature Review

1.1 Introduction

Once limited almost exclusively to aerospace applications, the use of composite

materials has become widespread among many high performance industries. Hydraulic

fracturing applications in the petroleum industry are demanding components, including

pipes, to meet higher production rates and stricter OSHA regulations. Advances in the

last decade of the quality and capabilities of resin, fiber, and fabrication equipment and

processes allow for more conversions from metal to composites [1]. Piping systems are

required to sustain high pressures, impact, rugged handling, and harsh environmental

conditions such as corrosion and temperature. Fluids used in hydraulic fracturing are very

abrasive because they are loaded with sand and they may be quite corrosive too.

Engineers are turning to advanced materials to meet tough design goals and are choosing

composites as solutions to weight and durability problems.

The combination of a reinforcing material embedded in a matrix form a composite

material. The reinforcing material is usually stronger and stiffer than the matrix. An

example of modern composite construction is steel reinforced concrete, where steel is the

reinforcement and concrete is the matrix. In general, a composite material is anisotropic.

This means that the material’s specific mechanical, electrical, and thermal properties

differ depending upon the direction of the applied potential, be it pressure, voltage or

temperature [1]. This differs from conventional isotropic materials such as steel or

aluminum whose properties do not vary with direction.

2

One way to increase performance of the composite is to combine two or more

reinforcing materials in a common matrix to form a single hybrid laminate. The two

most common methods of hybrid construction include “intraply” where reinforcing

materials are mixed within a ply, perhaps by using special woven cloth, or “interply”

where each ply consists of not more than one reinforcing material [2]. The interply

construction method is more flexible and the material is more readily available, however

intraply construction potentially displays better laminate properties and may suffer less

from delamination. Hybridization allows the designer to obtain benefits of each

reinforcing material while potentially reducing cost by applying the most expensive

material only where needed.

Hybrids exhibit a response called the “hybrid effect,” which describes an

enhanced strain to failure as compared to a composite with only one reinforcing material

[3,4]. An analogous effect also occurs which is described as “enhanced energy

absorption to failure.” This effect has the property that the energy absorbed by the hybrid

can theoretically exceed that absorbed in an identically constructed composite consisting

of only one of the reinforcing materials [5]. This derivative of the hybrid effect results in

a more robust laminate that fails gradually, not catastrophically, as the higher modulus

fibers fail before those with a lower modulus.

Hybridization can be applied selectively to complex structures for enhanced

benefits. A successful design approach in combined loading applications is to align high

modulus fibers in the direction of the maximum principle stress and low modulus fibers

in the directions of the minimum principle stresses [5]. Hybrid construction may provide

increased fatigue and impact strength properties. The addition of high modulus fibers to

3

low modulus fibers substantially improves the fatigue properties of the low modulus

material. Conversely, the addition of low modulus fibers to high modulus fibers

improves the impact strength of the high modulus material [6].

This research focused on the design, analysis, and fabrication of a hybrid

steel/composite discharge pipe to replace an existing all-steel pipe used by the

Halliburton Company. Hybridization of a metal liner with carbon and glass fiber

composite allows the following objectives to be reached:

1. Corrosion and abrasion resistance of steel as good as the conventional pipe.

2. Almost double the strain to failure of the steel liner by using autofrettage.

3. Lower weight.

4. Impact and handling resistance using glass-fiber composite over-wrap.

Three significant factors were to be met to satisfy the design standards. The first

requirement was to satisfy OSHA standards, which limit a man to carry no more than 50

lbs. This is a significant reduction in the weight of the original 105 lb steel pipe. The

second requirement was to withstand a maximum test pressure of 22.5 ksi and low cycle

fatigue strength of 15.0 ksi. The third requirement was to meet or exceed the physical

requirements of the work environment, such as impact, abrasion, and the joint makeup of

composite-metal interfaces. From the onset it was understood that a hybrid pipe keeping

the standard Weco fittings might not reach the low 50 lb objective. However, the

standard fitting was kept to allow for installation of the hybrid pipe in normal field

conditions. Replacing the Weco fittings by lighter ones was relegated to Phase II of this

project.

4

1.2 Literature Review

There is a vast amount of research on the subject of composite materials and their

applications. A brief review of composites, autofrettage in structures, and hybrid

composite construction is given here.

1.2.1 Composite Materials

Engineers are turning to advanced materials to meet tough design goals and are

choosing composites as solutions to weight and durability problems. While there has

been a steady increase in the use of composites in industry it has not replaced its heavier

standard engineering material counterparts such as aluminum and steel. An aluminum

alloy used in aerospace applications will have a yield strength near 70 ksi at a specific

gravity of 2.8 whereas a good carbon fiber reinforced plastic (CFRP) laminate in

unidirectional form can exhibit a tensile strength close to 435 ksi at a specific gravity of

1.6 [7]. While unidirectional CFRP has higher strength and lower weight than aluminum,

its mechanical properties in directions other than along the fibers are very low. One of

Boeing’s twin jets, the 777, was the corporation’s first commercial airplane with a

primary structure of composites [8]. Boeing engineers shaved 2600 lbs off the aircraft’s

structural weight. Nearly 9% of the plane’s structural weight consists of composites, ten

times the amount used on the 757 and 767.

The investigations of Potter et al. [7] determined there are two basic responses

that the aerospace community can make to further develop its market place. The first is

to develop lower cost manufacturing processes. The second is to attempt to apply new

thinking to the design process and to allow greater weight saving to be made so as to

5

move the competition between metals and composites to a new level without losing sight

of maintainability, damage, repair and costs.

Jim Shobert, President of Polygon Company, states that despite his company’s

experience in the composites field, he still must spend a lot of time educating engineers.

He maintains that the “metal mentality” must be fought and engineers must understand

that parts that are produced with composites may or may not resemble the metal part it

replaces. As a result, Polygon applications engineers work with design engineers to

explain the special properties and advantages of composites. Recent Polygon projects

have resulted in improved orthopedic fixators with a 20% reduction in weight from the

conventional stainless steel/aluminum construction by replacing metal crossbar section

with CFRP. The new design allows radiolucency so physicians can x-ray through the

device to monitor bone growth and healing [9].

Harvey and Kremer [10] states that the use of composite materials in cryogenic

fuel lines will present important weight savings for the Reusable Launch Vehicle (RLV).

Their research funded by NASA developed an all composite 12 inch diameter fuel line

capable of carrying liquid hydrogen at cryogenic temperature. The fabricated part weighs

less than 20% of a ‘state of the art’ fuel line and was successfully tested. Such weight-

saving capabilities prove that composites are an extremely valuable engineering material.

1.2.2 Autofrettage

Autofrettage is a pre-stressing technique, which for metal lined composite

pressure vessels consists of internally pressurizing the vessel until the metal is stressed

beyond its elastic range and therefore upon release of the load the composite introduces

6

residual compressive stresses in the liner. This procedure produces increased yield

strength in the metal and extends its usable elastic range.

In situations where fatigue life may not meet design goals, the use of an

autofrettage that introduces beneficial residual compressive stresses may provide a

solution. Segall [11] et al. investigated the feasibility of the fatigue life of thick-walled

cylinders with cross-bores by using a localized autofrettage technique. This technique

utilized the high stress concentration at the cross-bore to induce localized residual

stresses using relatively low internal pressures. The researchers used elastic-plastic finite

element (FE) calculations in conjunction with an elastic fracture-mechanics model of a

quarter-circular crack situated at the intersection of the cross-bore and the cylinder inner

diameter to conservatively calculate the extent of the fatigue life improvement. Results

showed significant improvement in cylinder life due to the localized residual stresses.

Another important advantage of a localized technique is that it will allow an autofrettage

after the cylinder has been machined to its final dimensions.

In a study on the fatigue life of cannon tubes with evacuator holes, Underwood et

al. [12] measured the effects of various amounts of autofrettage by overstrain. It was

shown that the measured fatigue life and the initiation position of the fatigue crack along

the evacuator hole was affected by overstrain. By increasing the amount of autofrettage

the crack initiation was moved along the hole from a location near the inner radius of the

tube to a mid-wall position. Up to a four-fold increase in fatigue life was noticed with a

change from 0 to 100 percent overstrain.

Hussain et al. [13] investigated the redistribution of residual stresses of an

autofrettaged tube due to geometrical changes such as keyways, rifling, cracks, etc. Their

7

research produce a method to simulate partial autofrettage residual stressed in thick-

walled cylinders. The technique developed provides a means of incorporating

redistributed residual stress into the stress analysis of autofrettaged cylinders. Such an

analysis method may be necessary to better understand the effects of geometrical

discontinuities on an overstrained pressure vessel.

Finite element methods were employed by Feng et al. [14] to model low-

temperature autofrettage of smooth thick-walled tubes of austenitic stainless steel AISI

304 L. The research objective was to show the greater efficiency of low-temperature

autofrettage over the same process at room temperature. It was theorized that at lower

temperatures, a higher beneficial residual compressive hoop stress would be introduced at

the inner part of the tube. Based on FE calculations, it was concluded that the low-

temperature process is a better solution and should more significantly enhance the

resistance to fatigue.

Autofrettage of aluminum-lined composite pressure vessels for compressed

natural gas has been discussed in [2] among others. Liu and Hirano [15] discussed the

design of fiber reinforced plastics (FRP) pressure vessels with load-carrying metallic

liners. The design concept included autofrettage to generate compressive residual stress

in the liner, which resulted in an increased usable elastic range and a higher yield stress.

Their research established an outline design approach and a method of detailed analysis

including the use of finite element methods. This resulted in a higher structural

efficiency for FRP pressure vessel design. The outcome from experimental testing

showed good agreement between actual and predicted burst pressures.

8

1.2.3 Hybrid Composite Structure

Hybrid composites are an important engineering material. A hybrid material

usually contains two or more types of fibers interlaminated or intermingled in a common

matrix. Hybrids have several advantages, such as the improvement of crack-arresting

properties, fracture toughness, and cost reduction by decreasing the amount of the more

expensive fiber. Research on hybrid composites had grown rapidly in recent years as

reviewed by Fukada and Chou [16]. Their work examines the load redistribution in a

hybrid composite sheet due to fiber breakage. The stress concentration factors of a

unidirectional hybrid composite with discontinuous fibers were calculated using a shear-

lag analysis. The result of the analysis indicated that in a hybrid composite containing

both high modulus and low modulus fiber, the stress concentration factor on the high

modulus fibers adjacent to a crack is lower than that in an all-high modulus fiber

composite for the same number of fractured fibers. Thus it is possible for the high

modulus fibers in a hybrid composite to sustain higher loading and elongation than in the

all-high modulus fiber composite, and a “hybrid effect” could be realized.

Karbhari et al. [17] determined the progressive crush response of braided tubes is

significantly affected by hybridization. Both the use of different types of fibers in

combination (glass, carbon and Kevlar) and different yield rovings were studied.

Triaxial braiding was shown to be the most efficient while optimum performance was

reached through the use of carbon fibers in the axial direction. It was seen that the use of

axial fibers in the braid architecture significantly increased the crush performance as well

as retaining post-crush integrity. The best performance was shown by the glass-carbon

and Kevlar®-carbon hybrids, where the carbon fibers were used in the axial direction,

9

with movement constrained by the glass or Kevlar braided yarns. Based on their results,

it is clear that significant tailoring of crush performance and crush mechanisms is

possible through hybridization.

A general mathematical formulation by Dhillon et al. [18] for the optimum design

of unstiffened and stiffened, composite, hybrid plate girders. Using the generalized

geometric programming (GGP) technique, the composite-hybrid-plate-girder problem

was formulated as a mathematical problem that uses the weight of the girder as the

objective function, with the section properties and strengths providing the problem

constraints. It was concluded that GGP provides an effective method for the design of

composite hybrid plate girders, offering savings in cost and design time and

demonstrating the cost effectiveness of web stiffeners in plate girder design.

Kim and Mai [19] studied the stress transfer in a multiple fiber composite

subjected to uniaxial tension. The model composite was treated as a three-cylinder

assemblage, which consisted of a central fiber, a matrix annulus and a composite

medium. The researchers conducted a parametric study and found that fiber

fragmentation becomes increasingly difficult as the stiffness of the average composite

medium increases. Conversely, the interfacial debonding becomes easier as this medium

is stiffened. These findings imply that for aligned discontinuous fiber composites the

stability and the energy absorption capability of the fracture process can be enhanced by

increasing the fiber volume fraction and the elastic modulus of the matrix.

The efforts of Chaudhuri and Garala [20] focused on improving the compressive

strength of CFRP by using a hybrid carbon/glass commingling concept. It was

determined that the formation and propagation of fiber kink bands at the microscopic

10

level (triggered by the fiber misalignment and waviness defects formed during the

manufacturing process) leading to a shear crippling failure at the macroscopic level, is the

dominant compressive failure mode. The researchers theorized that one way to improve

compressive strength is through the use of a commingled (at the tow level) hybrid fiber

system. Experimental data suggested enhancement of the compressive and flexural

strengths of the composite material even with a small percentage (15%) of glass fibers in

commingled hybrid composites. More significantly, inspection of the failed compression

test coupons demonstrated that this small amount of glass fibers is effective in changing

the failure mode away from the catastrophic kink band failure mode.

Hybrid construction may allow a designer to increase laminate stiffness without

sacrificing much strength. Analysis by Glenn et al. [5] showed that hybridizing glass

with small amounts of carbon initially resulted in reduced laminate strength. However, at

around 30% carbon concentration, analysis showed that the hybrid strength recovered

70% of the pure glass strength while stiffness exceeded that of pure glass by a 100% for

low modulus carbon.

It is clear that hybrid composite materials can be beneficial to the design of a

structure. The addition of strong fibers to weak fibers can be advantageous, but it is

inferred that the weaker fibers can decrease the strength of a laminate of strong fibers. It

is noted that great care must be taken in designing a hybrid composite to maximize the

use of the positive qualities of the various materials.

11

Chapter Two

Initial Design and Analysis

The steel pipe used by Halliburton Company has a wall thickness of 0.31 inch, an

inner diameter of 2.0 inches, and a length of 120 inches. The pipe has Weco 1502

hammer unions as shown in Figure 2.0.1. Initially, it was decided that making

modifications to the existing pipe would simplify fabrication of the new design. The pipe

would be turned down on a lathe to a specified diameter consistent with the wall

thickness of the new design, and then filament wound with carbon fibers and epoxy resin.

It was recognized that the pipe would undergo low cycle fatigue during operation,

therefore autofrettage was desired. The goal was to achieve the largest elastic range

possible. Therefore the composite was to be designed to stress the steel to within 95% of

compressive yield once the autofrettage pressure is removed. This would almost double

the effective elastic region of the stress-strain curve. Figure 2.0.2 shows the stress

resultant (stress multiplied by pipe thickness) versus strain curves for the steel pipe,

composite and the steel after yield for hoop stress. It was desired to autofrettage the pipe

at 22.5 ksi, which is the test pressure required by Halliburton. This is also 1.5 times the

working pressure.

Computer aided FEA was used to meet the complex analytical demands of the

project. SDRC® I-DEAS® was used jointly with ABAQUS® for most of the two-

dimensional analyses.

2.1 Steel Axisymmetric Model

To validate the FEA software for the design of the hybrid pipe, an I-DEAS®

model, all_steel.mf1, of the original steel pipe was developed and solved. An analysis

12

was performed using an axisymmetric finite element model (FEM). The FEM consisted

of two-dimensional axisymmetric elements, which act like three-dimensional solid

elements that revolve around a specified axis. This type of model was chosen because it

requires far less elements than a three dimensional model and therefore greatly reduces

the time needed to solve.

The geometry of the model consisted of a simplified longitudinal cross-section of

the pipe Figure 2.1.1. As seen in the figure, this was modeled as one fitting and a 20 inch

section of pipe with constant thickness. The end of the pipe with constant thickness was

restrained from having longitudinal translation, while the rest was free to expand and

elongate. An internal pressure load was simulated by applying a distributed load on the

“element free edges” closest to the axis of revolution, and a longitudinal force at the

pipe’s free end. Figure 2.1.2 shows the meshed model with boundary conditions. The

longitudinal force, which simulated the axial pressure load was calculated using

2longF r pπ= (2.1.1)

where r is the inner radius of the pipe and p is the applied pressure. The internal pressure

was 30.0 ksi. The elastic material properties of the elements were consistent with those

of generic isotropic steel with an elastic modulus of 30000 ksi and a Poisson’s Ratio of

0.29. The plastic material properties were defined by a yield strength of 93.5 ksi, an

ultimate strength of 115 ksi and 21% elongation at failure.

A second FEA software package was used to reach a solution for this model.

ABAQUS® was chosen due to its ability to solve quickly as well as its ability to perform

elastic-plastic analyses, which was crucial to designing the autofrettage process. The

solver in SDRC® I-DEAS® is not as powerful and is much slower than ABAQUS®. The

13

model was exported from I-DEAS® into an input file called all_steel.inp and solved using

ABAQUS®. The solution to the model was imported back into I-DEAS® for post

processing.

The maximum Von Mises stress in the steel, displayed by I-DEAS®, was 96.4 ksi.

The Von Mises stress is defined as [21]

( ) ( ) ( )2 2 2

12von mises I II I III II IIIσ σ σ σ σ σ σ = − + − + −

(2.1.2)

where σI, σII and σIII are principal stresses equal to σx, σy and σz respectively for internal

pressure loading. This result was conservative compared to the actual tests of the pipe.

The reason for the discrepancy was because the finite element model had just over 50

elements, resulting in a coarse mesh that produced a stiff representation of the pipe. The

solution was satisfactory and the method was deemed suitable for the analysis of the steel

and composite hybrid.

2.2 Composite Material Selection and Bi-Directional Laminate Design

Initially, AS4 carbon-epoxy composite was chosen because of its material

properties and relatively low cost. Orthotropic elastic material properties for AS4 in a

unidirectional composite were recorded by Barbero [22] and are shown in Table 2.2.1.

Some of these properties are derived as follows assuming the unidirectional composite is

transversely isotropic

3 2

13 12

13 12

32 23

31 21

221 12

1

E EG Gv vv vv v

Ev vE

=====

=

(2.2.1)

14

Microsoft® Excel spreadsheet as4_bi-directional.xls was used to calculate the

equivalent orthotropic elastic material properties of a bi-directional composite lay-up (i.e.

±45°, ±62°). The calculations were performed for a two-ply laminate with each layer

having a unit thickness.

The stiffness matrix [C] was computed for a 0° unidirectional AS4 composite

[ ]

11 12 13

12 22 23

13 23 33

44

55

66

0 0 0

0 0 0

0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

C C C

C C C

C C CC

C

C

C

=

(2.2.2)

with the components calculated in terms of orthotropic elastic material constants as

shown below [23]

11

12

13

22

23

33

44

55

66

23 32

2 3

21 31 23

2 3

31 21 32

2 3

13 31

1 3

32 12 31

1 3

12 21

1 2

23

13

12

12 21 23 32 13 31 21 32 13

1 2 3

1-

1-

1-

1- - - - 2

C

C

C

C

C

C

C

C

C

v vE E

v v vE E

v v vE E

v vE E

v v vE E

v vE E

GGG

v v v v v v v v vE E E

∆ =

=∆

+=

∆+

=∆

=∆

+=

∆

=∆

===

The stiffness matrix [C(θ)] was calculated for a fiber orientation of θ using the

transformation matrices [T] and [T]T (transpose of [T]) as

[ ] [ ] [ ]( ) TC CT Tθ = (2.2.3)

15

where [T] is

[ ]

2 2 21 1 1 1 1 1 1 1 12 2 22 2 2 2 2 2 2 2 22 2 23 3 3 3 3 3 3 3 3

2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3

1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3

1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2

2 2 22 2 22 2 2

l m n m n l n l ml m n m n l n l ml m n m n l n l m

Tl l m m n n m n n m l n n l l m m ll l m m n n m n n m l n n l l m m ll l m m n n m n n m l n n l l m m l

= + + +

+ + +

+ + +

(2.2.4)

and the components are defined as

1

2

3

cos

sin

0

l

l

l

θθ

== −=

1

2

3

sin

cos

0

m

m

m

θθ

===

2

3

1 001

n

n

n

===

The stiffness matrix of the second layer, [C(−θ)],was calculated as described above with a

negative theta. The stiffness matrix of the bi-directional laminate, [C(±θ)], was produced

by combining the components of [C(θ)] with those of [C(−θ)] as described below

( ) ( )

( )

2ij ij

ij

tC tCC

t

θ θθ

−± +

= (2.2.5)

where t is the thickness of one layer.

The compliance matrix [S] is the inverse of the stiffness matrix

[ ] 1( )S C θ −± = (2.2.6)

The compliance matrix is described in terms of orthotropic elastic material constants as

[ ]

1312

1 1 1

2312

1 2 2

13 23

1 2 3

23

13

12

1 0 0 0

1 0 0 0

1 0 0 0

10 0 0 0 0

10 0 0 0 0

10 0 0 0 0

vvE E E

vvE E Ev vE E E

S

G

G

G

− − − − − − =

(2.2.7)

16

The equivalent elastic material properties of the laminate were calculated from the

components of the compliance matrix. These are defined as

1

2

3

11

22

33

1

1

1

E

E

E

S

S

S

=

=

=

12

13

66

55

2344

1

1

1

G

G

G

S

S

S

=

=

=

12 12 1

13 13 1

23 23 2

v S E

v S E

v S E

= −

= −

= −

32 32 3

21 21 2

31 31 3

v S E

v S E

v S E

= −

= −

= −

(2.2.8)

Equations (2.2.2) through (2.2.8) were used to determine the equivalent

orthotropic material properties of AS4 for each bi-directional lay-up from 0° to 90° in 5°

increments (i.e. 0°, ±5°, ±10°… ±85°, 90°). An example of the orthotropic material

properties before and after transformation is shown in Table 2.2.1. These material

properties were then used to determine the required composite thickness for the

longitudinal and hoop stresses.

Derivations were performed to determine the thickness of the composite to

autofrettage the steel pipe to 95% of compressive yield. These equations describe the

stress resultant versus strain graph in Figure 2.0.2.

First, it was assumed that the strain in the composite is equal to the strain in the

steel

c sε ε= (2.2.9)

The yield stress of steel was denoted by σyield and the yield strain by εyield. The yield strain

εyield was determined from

yieldyield

sEσ

ε = (2.2.10)

where Es is the modulus of elasticity of steel. Since the composite is linear and elastic,

the stress in the composite for any load is

17

c c hoopEσ ε= (2.2.11)

where Ehoop is the modulus of elasticity of the composite in the hoop direction (90° from

the longitudinal axis). The stress in the in the hoop direction of a pipe is calculated from

2hpd

tσ = (2.2.12)

where p is the applied internal pressure, d is the inner diameter of the pipe and t is the

wall thickness. The stress resultant N, is the tensile force per unit length, along the edge

of a plate, and is calculated as

N tσ= (2.2.13)

The stress resultant in the hoop direction of the hybrid pipe was derived by substituting

(2.2.12) into (2.2.13), as shown

2h hpdN tσ= = (2.2.14)

Due to the hybrid design of the pipe, Nh is a function of Nc and Ns, which are the hoop

stress resultants in the composite and steel respectively. This is essentially a force

balance equation as shown below

h c sN N N= + (2.2.15)

where

s yield sN tσ= (2.2.16)

and

c c hoopN tσ= (2.2.17)

where t hoop is the thickness of the composite. For the autofrettage load, the components

Nh and Ns are known, equation (2.2.15) can be rearranged to form

Q h scN N N= − (2.2.18)

18

If the thickness of the composite is chosen, then the hoop stress can be found from

QQ

hoop

cc

Nt

σ = (2.2.19)

then the hoop strain in the composite and the steel can be determined from

QQ

hoop

c

Eσ

ε = (2.2.20)

The drop of hoop strain, ∆εc2, in the composite up to the point when the steel is at 95% of

compressive yield stress has two components, the drop from autofrettage stress to zero

stress and the 0.95 drop to 95% of compressive yield,

( )2 1 0.95 1.95c yield yieldε ε ε∆ = + = (2.2.21)

as seen in Figure 2.0.2. From this number, the drop in hoop force per unit length, ∆Nc2, is

2 2c c hoopN tσ∆ = ∆ (2.2.22)

where ∆σc2 is the drop in hoop stress in the composite

2 2c hoop cEσ ε∆ = ∆ (2.2.23)

Equation (2.2.22) is also represented by

2c Q Rc cN N N∆ = − (2.2.24)

where NQc was found from (2.2.18) and NRc is

.95R yield scN tσ= (2.2.25)

The thickness of the composite for the hoop stress criteria was determined by combining

equations (2.2.22) and (2.2.23) to get

2

2

choop

hoop c

NtE ε

∆=

∆ (2.2.26)

which was expanded to

19

1.95

21.95

yield s

hoopyield hoop

pd tt

E

σ

ε

−= (2.2.27)

The above derivation was based on the drop in hoop strain and the drop in the

hoop stress resultant. A second derivation was performed to confirm the first. It was

based on the fact that the hoop stress resultants in the composite and steel after

autofrettage must be equal and opposite as seen in Figure 2.0.2. They must also be equal

to 95% of the compressive yield stress resultant of steel as shown

.95R R sc sN N N= = (2.2.28)

this was expanded using (2.2.13) to form

.95R hoop yield sc t tσ σ= (2.2.29)

The composite thickness for autofrettage in the hoop direction was found from (2.2.29) to

be

.95 yield shoop

Rc

tt

σσ

= (2.2.30)

where σRc is

( )1.95R Q yield hoopc Eσ ε ε= − (2.2.31)

and εQ was determined from equations (2.2.14) through (2.2.20) to be

2 yield s

Qhoop hoop

pd t

t E

σε

−= (2.2.32)

By substituting (2.2.31) and (2.2.32) into (2.2.30) and rearranging, thoop becomes equation

(2.2.27) and thus reinforces the first derivation. Comparison between results based on

(2.2.27) and FEA were not favorable because the simplified analysis neglects the

20

longitudinal stress. Therefore, a safety factor of 1.95 was applied resulting in the

modified hoop thickness

1.95

2 yield s

hoopyield hoop

pd tt

E

σ

ε

−= (2.2.33)

Equation (2.2.33) was used in Microsoft® Excel to calculate the required

thickness of the composite to autofrettage the pipe in the hoop direction. This value was

calculated for a steel pipe with a two-inch inner diameter and wall thickness of 0.155

inch, which is half of the thickness of the original pipe. The yield strength of the steel

was chosen to be 52 ksi. The autofrettage pressure, p, was 22.5 ksi. The composite’s

modulus of elasticity in the hoop direction, Ehoop, was calculated for 19 different bi-

directional fiber orientations ranging from 0° to 90° in 5° increments. The value of thoop

was calculated for each of the 19 cases and is shown in Table 2.2.2.

The equations to calculate the thickness of the composite for longitudinal load

were derived. The static equilibrium equation of the pipe is

c sF F F= + (2.2.34)

where F is the longitudinal force due to the internal pressure load

2F r pπ= (2.2.35)

Fc and Fs are the reaction forces in the composite and steel respectively

c long cF Aσ= (2.2.36)

s yield sF Aσ= (2.2.37)

where Ac and As are the cross-sectional areas of the composite and steel respectively. By

substituting equations (2.2.36) and (2.2.37) into equation (2.2.34), the equilibrium

equation becomes

21

long c yield sF A Aσ σ= + (2.2.38)

This equation was rearranged to solve for Ac as shown below

yield sc

long

F AA

σσ

−= (2.2.39)

The stress in the composite, σlong, at σyield can be represented by

long yield longEσ ε= (2.2.40)

where Elong is the modulus of elasticity of the composite in the longitudinal direction. By

substitution, Ac is

2

yield sc

yield long

r p AA

Eπ σ

ε−

= (2.2.41)

The cross-sectional area of the steel is

( ) 2 2s sA r t rπ= + − (2.2.42)

The thickness of the composite was found by rearranging the following equation

( ) ( ) 2 2c s long sA r t t r tπ= + + − + (2.2.43)

to get

( ) ( )2clong s s

At r t r tπ

= + + − + (2.2.44)

where tlong is the thickness of the composite and the value for Ac in (2.2.44) comes from

equation (2.2.41).

The composite’s modulus of elasticity in the longitudinal direction, Elong, was

calculated for the same 19 bi-directional fiber orientations as described earlier. The

value of tlong for longitudinal loading was calculated for each of the 19 cases and is shown

in Table 2.2.2.

22

The composite thickness was plotted versus the bi-directional lay-up angle for the

longitudinal stress and the hoop stress as shown in Figure 2.2.1. The optimum fiber lay-

up angle was determined to be at the angle at which the two curves cross, approximately

±50°.

The weight per unit length of the steel pipe, ws, was calculated using the

following formula

( ) 2 212s s sw r t rρ π = + −

(2.2.45)

where ρs is the density of steel. The weight per unit length of the composite over-wrap is

( ) ( ) 2 212c c s c sw r t t r tρ π = + + − +

(2.2.46)

where ρc is the density of AS4 composite, tc is the thickness and is equal to either t hoop or

tlong. The total weight per unit length, wp, of the hybrid pipe is

p s cw w w= + (2.2.47)

The weight per unit length for thoop and tlong was plotted versus the bi-directional fiber

orientation θ as shown in Figure 2.2.2. The required composite thickness for the

optimum lay-up of ±58° proved to be quite large and would result in a hybrid pipe that

outweighs the original steel pipe. It was determined that a bi-directional lay-up resulted

in an inefficient use of composite material for this loading condition. Further analysis

was required to determine the optimum laminate design.

2.3 Three-Directional Laminate Design

To minimize the thickness of the composite, a three-directional lay-up was

considered. The thickness required to sustain hoop stress is minimized when fibers are

oriented at 90° from the longitudinal axis. In the same manner, the minimum thickness

23

required to withstand longitudinal stress is when fibers are oriented at 0°. Filament

winding does not have the capability to place fibers at 0°, therefore an orientation of ±20°

was chosen for the longitudinal component. This combination of +20°, -20° and 90° was

designed using Microsoft® Excel.

A new spreadsheet original_hybrid_as4_tri-directional.xls was created to

calculate the transformation matrices for a three-directional composite. The procedure in

section 2.2 for determining the equivalent orthotropic material properties was modified

for the tri-directional laminate. Three stiffness matrices, [C(20)], [C(−20)] and [C(90)], were

computed for the unidirectional layers. The stiffness matrix of the tri-directional

laminate, [C(±20,90)], was produced by combining the components of [C(20)] with those of

[C(−20)] and those of [C(90)] as described below

(20) ( 20) (90)

( 20,90) 20 20 90

20 20 90

ij ij ijij

t C t C t CC

t t t

−± −

−

+=

++ +

(2.3.1)

where t20 and t-20 were each equal to half of tllong calculated at ±20° and t90 was equal to tihoop

calculated at 90°. The compliance matrix was formed using (2.2.5) and then the

equivalent elastic material properties were calculated using equation (2.2.7). The

calculated orthotropic material properties are based on the coordinate system of the

unidirectional composite, which is different from the coordinate system in ABAQUS®.

Figure 2.3.1 depicts the material and ABAQUS® coordinate systems and Table 2.3.1

describes the relation between the properties from the two. These properties as well as

lay-up thickness are listed in Table 2.3.2.

Computer Aided Design Environment for Composites (CADEC©, 1998) was used

to determine the First Ply Failure (FPF) values, stresses at which the composite begins to

24

develop cracks in the resin, and Fiber Failure (FF) values, stresses at which catastrophic

fiber failure occurs. The elastic material properties of unidirectional AS4 were used

along with the shear, tensile, and compressive strength values of the resin and fiber.

Figure 2.3.2 is the laminate definition window from CADEC© describing the lay-up. The

program was used to estimate the FPF and FF in the hoop and longitudinal directions for

a composite with specified lay-up angles and layer thickness. Table 2.3.3 shows the

values of FPF and FF for the tri-directional design described in Table 2.3.2.

2.4 Hybrid Steel/Composite Axisymmetric Model

A new axisymmetric FEM, original_hybrid.mf1, was created to analyze the

steel/composite design in the same manner as the steel FEM in section 2.1. This new

model incorporated two separate layers as shown in Figure 2.4.1. The inner layer was

0.155 inch steel with an outer 0.264 inch composite layer. The two layers were separated

by a 0.005 inch gap. The actual pipe would not have a gap between the steel and the

composite, but it was modeled this way to simplify the application of gap elements

between the two materials. Gap elements prevent the parts from passing through one

another when one part is displaced into the spaced occupied by another. These elements

were attached between two nodes, one on each part, having close proximity (this

procedure is described in Appendix A). Figure 2.4.2 shows the lower half of the meshed

model with boundary conditions and details of the gap elements. The gap elements will

allow the nodes to separate freely but prevents intersection.

The pressure load was applied and the parts were restrained as described in

section 2.1. The elastic material properties of the steel elements were defined

consistently with those of generic isotropic steel. The orthotropic material properties,

25

engineering constants [24], of the composite and the plastic material definition of the

steel were defined after exporting the model to ABAQUS® in file hybrid1.inp.

Plastic material properties of 4130 steel were attained from Shigley and Mischke

[21], but it was unclear what type of heat treatment would be used on the design, so

initially the plastic properties of 4130 annealed were chosen for the analysis. The input

file was modified to define the yield strength as 52 ksi and the plastic region of the stress-

strain curve to be from 52 ksi to 81 ksi with a 28% elongation at rupture. The orthotropic

elastic material properties of the composite were changed to be consistent with those

calculated in Excel. The load step was modified into three steps. The first load step

increased from 0.0 to 22.5 ksi internal pressure, which is the autofretage load to yield the

steel. The second load step decreased from 22.5 back to 0.0 ksi, which shows how much

the steel is compressed under the composite. The final load step increased from 0.0 to

15.0 ksi internal pressure, which is to simulate working pressure under normal conditions

after the autofretage process is complete. The ABAQUS® input file is displayed in

Appendix B.

The model was input into the ABAQUS® solver. The results were recorded in a

“.fil” file which was imported into I-DEAS® for post processing. The file was translated

into an I-DEAS® Universal file and then opened for viewing. The post processor in

I-DEAS® is icon based which makes it more user friendly than the text command based

post processor in ABAQUS®. Once in I-DEAS®, the result file was found to be missing

and upon inspection of the data and message files created by ABAQUS®, it was

discovered that the model was unable to solve. Error messages indicated that the steel

elements were experiencing strains, which exceeded the defined stress-strain curve in the

26

material properties section of the input file. The solver was unable to calculate logical

results and subsequently terminated the process before reaching a solution.

In an attempt to reach a temporary solution, the plastic region of the stress-strain

curve was redefined from 52 ksi to 200 ksi instead of 52 ksi to 85 ksi. The ABAQUS®

model was solved again producing the same errors; however, to less of an extent as the

first run. The stress-strain curve was modified several more times producing the same

errors. Finally, the curve exceeded 1000 ksi and a solution was reached. The model was

translated into I-DEAS® and the results viewed in its post processor. At this time, the

reason behind the errors became clear. The steel was elongating freely, underneath the

composite, to the point of catastrophic failure. The end of the composite was not

fastened to the steel in a manner in which the longitudinal stress could be transferred

from the steel into the composite. This simple oversight was corrected through the use of

coupled degrees of freedom (Coupled DOF), see Appendix A. This is a means by which

one or more slave nodes are made to conform to a specified set of translations and/or

rotations dependent on one master node. This was done in I-DEAS® on 8 pairs of nodes

at the end of the composite closest to the fitting. The steel nodes were defined to be the

independent master nodes, with each one coupled with the closest available free node on

the composite. Details of the Coupled DOF can be seen in Figure 2.4.3.

The model was then exported to ABAQUS® and the plastic material properties of

the steel were set to the correct values. A solution was reached and the message and data

files were examined and showed zero errors. The model was imported back into

I-DEAS® and viewed in the post processor. The Von Mises stress values for the steel

were recorded at each load step, but Von Mises is not a valid method for use with

27

orthotropic materials. It is not out of the ordinary for the material properties of

composites to differ in all three coordinate planes, such is the case with this hybrid

design. Therefore, it was necessary to view the X, Y and Z stresses separately for the

composite elements. The analysis was focused mainly on the hoop stresses (Z-axis) and

the longitudinal stresses (Y-axis). There was a high stress concentration at the location of

the longitudinal force because the load was not well distributed over several nodes,

therefore the stress values near that location were neglected. The max stresses in the

composite’s hoop and longitudinal directions were recorded and the safety factor, S.F.,

for the steel at yield and ultimate as well as for the composite at FPF and FF were

calculated. The equation for the factor of safety is

. . limitS F σσ

= (2.4.1)

where σ is the stress in the steel or composite as calculated by I-DEAS® and σlimit is the

limiting strength criteria as shown in Table 2.4.1. The steel elements exceeded the yield

point during the first load step and the composite elements did not reach First Ply Failure.

The results of the second load step, 0.0 ksi, showed that the steel elements were under

compressive stress and reached 87.5% of compressive yield. The third load step, 15 ksi,

showed good results with a 2.37 factor of safety to yield the steel and 3.88 S.F. for

failure. The stresses and factors of safety at each load step are shown in Table 2.4.2.

2.5 Optimization of the Hybrid Design

In order to optimize the weight of the design, Excel spreadsheet

as4_&_t800_with_52ksi_&_100ksi.xls was created. It calculated the required composite

thickness when the steel thickness varied from 0.31 inch to 0.01 inch, in 0.01 inch

increments. It was used to compare two different types of 4130 steel with yields of 52 ksi

28

and 100 ksi. It also compared two different CFRPs, AS4 and T800. Four cases were

formed: AS4 with 52 ksi yield, AS4 with 100 ksi yield, T800 with 52 ksi yield and T800

with 100 ksi yield.

The same methods as described in the previous sections were used for computing

composite thickness due to each specified steel thickness. The [±20°, 90°] design was

used in all scenarios. The thickness of steel was plotted versus the composite thickness

needed to perform the autofrettage process, see Figure 2.5.1. From this plot it can be

seen that for steel yield strength of 52 ksi, the pipe cannot be autofrettaged when ts is

greater than 0.21 inch (the composite would have zero thickness). The same is true for

100 ksi steel with a thickness greater than 0.11. Figure 2.5.2 shows the steel thickness

versus the weight of steel and the hoop-wound composite. It became clear from this

graph that increasing the steel yield strength decreases the weight of the pipe. A third

graph, Figure 2.5.3, was created to show the thickness of the steel versus the safety factor

for the hoop-wound fibers at autofrettage pressure. The safety factor was found from

max. .h

NS FN

= (2.5.1)

where Nh was found from (2.2.14) and the maximum stress resultant, Nmax, is

max hoops FFN N N= + (2.5.2)

Equation (2.2.13) was used to calculate the stress resultants of the steel at yield and of the

hoop-wound composite at Fiber Failure, Ns and NFFhoop respectively.

The factor of safety graph was needed to choose a steel and composite

combination with the same performance standards as the original pipe. From this plot, it

was realized that a thickness range existed where the 52 ksi steel had a factor of safety

below 1.0 and would not withstand the autofrettage load. It was also noticed that for the

29

100 ksi steel, there existed a range where the thickness could be reduced without the need

for any composite to be added; however, the safety factor was reduced linearly to 1.0.

Secondly, it was noted that beyond this region the safety factor continued to decrease

below 1.0. Once the steel dropped below a certain thickness, the safety factor increased

and passed the 1.0 mark. This plot revealed that for some steel thickness, more

composite material was needed to keep the pipe from bursting than was needed for

autofrettage.

The spreadsheet was modified to calculate the thickness of the hoop composite

needed to keep the pipe from failing

h shoop fail

hoop

N NtFF−

−= (2.5.3)

This equation comes from rearranging (2.2.15) and was calculated for each thickness of

steel. Excel compared the composite thickness needed to autofrettage against the

thickness needed to prevent failure and chose the greater of the two. This changed the

safety factor plot as shown in Figure 2.5.4. The first thickness range of the 100 ksi steel

remained the same with the safety factor decreasing to 1.0 as the steel thickness

decreased. At this point, composite material was added to keep the pipe from failing,

thus creating a region where the steel thickness decreased while the safety factor

remained at 1.0. After the thickness of the steel decreased below 0.10 inch, the safety

factor increased linearly since the composite material required for autofrettage was

greater than that needed to prevent failure. On the other hand, the 52 ksi steel required

the addition of composite even at its thickest and produced a S.F. of 1.0 until the steel

thickness decreased below 0.22.

30

The safety factor of the original steel pipe was 1.5 when pressurized to 22.5 ksi.

It was desired that the hybrid pipe have approximately the same safety factor. As the

safety factor increased, the steel thickness decreased toward impractical dimensions.

Therefore, from the graph, a steel thickness of 0.07 inch for 100 ksi steel and AS4

composite was chosen for FEA because it had a factor of safety equal to 1.632. AS4 was

chosen because the high cost T800 carbon fiber did not afford a great difference in

calculated performance.

The lay-up angles and thickness from Excel were input into CADEC© to

determine the composite’s strength. The thickness and equivalent elastic material

properties of the optimized design are shown in Table 2.5.1. The orthotropic properties

were converted into the coordinate system used in ABAQUS® as previously described.

The FPF and FF values of the composite for the hoop and longitudinal directions are

shown in Table 2.5.2.

A new FEM was created in I-DEAS® according to the optimized design. It

followed the same form as the previous models, using two layers of axisymmetric

elements separated by gap elements. The thickness of the steel elements and the [±20°,

90°] composite elements followed Table 2.5.1. The boundary conditions and loads were

applied in the same manner as described for earlier models. The FEM was exported to

ABAQUS® to be edited and solved. The new composite material properties from Excel

and the plastic material definition for the steel were input. The ultimate stress for the

steel was chosen to be 118 ksi at 22% elongation [21]. As in the previous FEA, the

loading was divided into three steps and the model was solved.

31

After a solution had been reached, the model was imported into I-DEAS® to view

the results. Table 2.5.3 shows the stresses and safety factors at each load step. It was

determined that the composite was withstanding the loads and was allowing the steel to

yield in the first load step. The steel then reached 81% of compressive yield during the

second step. The model also faired well under the third load step, which is working

pressure after autofrettage. Although the stresses exceeded the First Ply Failure, the

composite did not reach Fiber Failure.

It was determined that the yield strength of the steel is an extremely important

factor with respect to weight reduction. The 100 ksi steel proved to be superior to the 52

ksi steel for this application. It was also determined that the weight of the pipe could be

reduced further by an increased fiber elastic modulus. When compared to AS4, T800

showed a minimal improvement in performance but this was overshadowed by its higher

cost. Therefore AS4 was determined to be the fiber of choice.

2.6 Bending Analysis

Through finite element analysis, the pipe was proven to perform under pressure

loads of 22.5 ksi. The following analyses were performed to determine the bending stress

under certain load cases and the maximum bending load for a simply supported beam.

The strength contribution of the thin-walled steel was neglected in these analyses in order

to simplify the calculations. All bending analyses were performed by hand.

The first load case simulated a situation in which a worker carries the pipe at its

midpoint. This was modeled as a beam with the moment of inertia of the composite

over-wrap calculated as

3I r tπ= (2.6.1)

32

where r is the inner radius of the composite over-wrap and t is its thickness. It was loaded

with a concentrated load, Wfitting, at each end, equal to the weight of the fittings, and a

distributed load along the entire length of the pipe to simulate the weight of the

composite plus the thin-walled steel. The weight of each fitting is 4.57 lbs. The

distributed load, wp, is the total weight per length of the hybrid pipe without fittings and

was calculated using (2.2.47). A single positive concentrated load in the middle of the

beam was used as the support point and was calculated as

2 fitting c sR W w l w l= + + (2.6.2)

where l is the pipe length between fittings. Figure 2.6.1 shows the pipe with the

described boundary conditions.

A shear diagram was plotted, Figure 2.6.2, and the maximum moment was equal

to one of the shaded areas enclosed by the x-axis and the curve in the shear diagram, as

calculated by (2.6.3).

max1

2 2 2 2fitting fittingl l RM W W = + −

(2.6.3)

The maximum stress, σmax, was calculated from

maxmax

M cI

σ = (2.6.4)

where c is the outer radius of the composite.

The analysis showed that the pipe would withstand this load case with an

extremely large safety factor of 95.

The second beam bending analysis was performed for three quarters of the pipe

cantilevered off of a platform, while the remaining 2.5 feet support the pipe. A negative

load, R2, was applied on the end resting on the platform and a positive resultant load, R1,

33

was applied two feet from that end to simulate the edge of the platform. A uniform

distributed load, wp, was applied on the entire length of the pipe simulating its weight per

unit length. Concentrated loads, Wfitting, were applied at each end of the pipe to simulate

weight of the fittings. Figure 2.6.3 describes this load scenario. A force balance equation

was created as follows

1 22 0y p fittingF w l W R R= − − + − =∑ (2.6.5)

This was rearranged to solve for R2 in term of the other components as

2 1 2p fittingR R w l W= − − (2.6.6)

The values of the resultants were found using the moment balance equation about R2, as

shown

2 1

3 5 04 8 4 4 8

p pR fitting

w wl l lM R W l = − + + =

∑ (2.6.7)

The value for R1 was found by rearranging the above equation as follows

1

34 54 8 4 8

p pfitting

w wl lR W ll

= + +

(2.6.8)

and R1 was found by back substitution into (2.6.6).

A shear diagram was drawn and used to find the maximum moment, which was

used in the bending stress equation. The shear distribution is shown in Figure 2.6.4.

Mmax was equal to the area of one of the shaded regions in the shear diagram as calculated

from

( )max 21

4 2 4 4fitting pl l lM W R w = + +

(2.6.9)

The maximum stress, σmax, was calculated from (2.6.4). This analysis resulted in a large

safety factor of 47.

34

The final bending analysis was for a simply supported pipe. This analysis was

useful for determining what would happen to the pipe if a worker stood or sat on it at it’s

midpoint. The model consisted of a beam loaded with a uniform distributed load equal to

the total weight of the composite and the steel. It had simply supported boundary

conditions and a concentrated load of 250 lbs applied midway between the pipe ends.

This load case is pictured in Figure 2.6.5.

The reaction forces, R1 and R2, were equal due to the symmetric boundary

conditions and were calculated by

1 2

2 2502

p fittingw l WR R

+ + = =

(2.6.10)

The shear distribution is shown in Figure 2.6.6 and was used to calculate the maximum

moment from the following

( )max1125

2 2 2 2 pl l lM w = +

(2.6.11)

The maximum stress, σmax, was calculated from (2.6.4). This analysis resulted in a

satisfactory safety factor of 8.1.

It was desired to determine the maximum load the pipe could withstand for the

simply supported beam scenario. A reverse calculation was performed by defining the

maximum allowable bending stress as equal to the longitudinal Fiber Failure value of the

composite as shown

max longFFσ = (2.6.12)

The maximum moment was determined by rearranging (2.6.4) to get

maxmax

IMc

σ= (2.6.13)

35

and the maximum allowable force, Fmax, was calculated by

max max2 12

2 2 2 pl lF M w

l = −

(2.6.14)

The calculated maximum force, using the equations above, was 2146 lbs. The maximum

force was also calculated using

max . .*F S F F= (2.6.15)

where F is the 250 lb load from the previous analysis and S.F. is 8.1. This resulted in a

maximum force of 2025 lbs, which is slightly conservative when compared to the results

from (2.6.14).

2.7 Conclusions

From the research and analysis recorded in this chapter it was concluded that:

• Finite element analysis using I-DEAS and ABAQUS with a two dimensional

axisymmetric model produces valuable results upon which design decisions can be

made.

• A bi-directional composite lay-up is not as efficient as a tri-directional laminate.

• The equation derived for determining the thickness of the hoop wound composite was

proven to be inaccurate and was increased by a factor of 1.95 to obtain good results

from the finite element analysis.

• Steel with higher yield strength is more efficient.

• The FEM of the tri-directional design predicted that the pipe would withstand the

22.5 ksi internal pressure and would be autofrettaged to produce a residual stress 81%

of compressive yield for a steel with a yield strength of 100 ksi.

36

• The bending analysis predicted that the pipe could withstand a load of over 2000 lbs

applied at the middle of the pipe with simply supported boundary conditions.

37

Table 2.2.1 – Orthotropic elastic material properties of AS4 in unidirectional and ±±±±20°°°° bi-directional lay-ups.

Unidirectional ±±±±20°°°° Bi-directional E1 = 2.060E+07 1.426E+07 E2 = 1.494E+06 1.684E+06 E3 = 1.494E+06 1.530E+06 G12 = 1.044E+06 2.823E+06 G13 = 1.044E+06 9.413E+05 G23 = 1.640E+05 2.669E+05 νννν12 =

0.270 1.109 νννν13 =

0.270 0.008 νννν23 =

0.290 0.258 νννν32 =

0.290 0.234 νννν21 =

0.020 0.131 νννν31 =

0.020 0.001

Table 2.2.2 – Required composite thickness to autofrettage 0.155 inch thick steel according to bi-directional fiber orientation ±θθθθ.

±θθθθ E hoop[psi] t hoop [in] E long [psi] t long [in] 0 1.494E+06 2.775 2.060E+07 0.061 5 1.504E+06 2.757 2.024E+07 0.062 10 1.535E+06 2.700 1.910E+07 0.065 15 1.592E+06 2.603 1.706E+07 0.073 20 1.684E+06 2.462 1.426E+07 0.087 25 1.823E+06 2.274 1.118E+07 0.109 30 2.032E+06 2.040 8.380E+06 0.144 35 2.347E+06 1.767 6.183E+06 0.191 40 2.821E+06 1.470 4.608E+06 0.251 45 3.536E+06 1.173 3.536E+06 0.319 50 4.608E+06 0.900 2.821E+06 0.389 55 6.183E+06 0.671 2.347E+06 0.456 60 8.380E+06 0.495 2.032E+06 0.515 65 1.118E+07 0.371 1.823E+06 0.565 70 1.426E+07 0.291 1.684E+06 0.603 75 1.706E+07 0.243 1.592E+06 0.632 80 1.910E+07 0.217 1.535E+06 0.651 85 2.024E+07 0.205 1.504E+06 0.662 90 2.060E+07 0.190 1.494E+06 0.666

38

Table 2.3.1 – Relation between orthotropic elastic material properties in the ABAQUS® coordinate system and the coordinate system used for calculations in Microsoft® Excel.

Excel ABAQUS®

E1 Ey E2 Ez E3 Ex G12 Gyz G13 Gxy G23 Gxz νννν12

ννννyz

νννν13

Not used

νννν23

Not used

νννν32

ννννxz

νννν21

Not used

νννν31

ννννxy

Table 2.3.2 – Initial tri-directional hybrid design describing composite and steel thickness and equivalent orthotropic elastic material properties using AS4 composite in a [±±±±20°°°°, 90°°°°] lay-up.

Ex = 1.677E+06psi

Ey = 6.229E+06psi

Ez = 1.464E+07psi

ννννxy =

0.0967

ννννxz =

0.0366

ννννyz =

0.0654

Gxy = 1.606E+06psi

Gxz = 4.093E+05psi

Gyz = 7.990E+05psi

t20 = 0.086in

t90 = 0.179in

t[20,90] = 0.264in

ts = 0.155in

σσσσs =

5.200E+04psi

39

Table 2.3.3 – First Ply Failure and Fiber Failure values for the initial tri-directional hybrid design using AS4 composite in a [±±±±20°°°°,90°°°°] lay-up.

Hoop Longitudinal FPF = 8.490E+04 3.425E+04 FF = 1.900E+05 8.990E+04

Table 2.4.1 – Description of limiting stresses and symbols for the steel and composite.

Material Calculated Stress Symbol Limiting Stress Symbol Yield Stress σyield Steel Von Mises

Stress σVon Mises Ultimate Stress σult

First Ply Failure FPFhoop Composite (hoop) Hoop Stress σhoop Fiber Failure FFhoop First Ply Failure FPFlong

Composite (long.) Longitudinal Stress σlong

Fiber Failure FFlong

Table 2.4.2 – Finite element analysis results for the initial tri-directional hybrid design incorporating

hoop thickness from flawed equation.

ts = 0.155, t[±±±±20°°°°,90°°°°] = 0.264 w/ 52ksi Steel Steel σσσσVon Mises [ksi]

σσσσYield [ksi]

S.F. σσσσUlt [ksi]

S.F. Test 52.80 52.00 0.98 85 1.61Zero 45.50 52.00 1.14 85 1.87Work 21.90 52.00 2.37 85 3.88

[±20,90] σσσσhoop [ksi]

FPFhoop [ksi] S.F. FFhoop [ksi] S.F. Test 68.10 84.90 1.25 190.00 2.79Zero 36.40 84.90 2.33 190.00 5.22Work 57.60 84.90 1.47 190.00 3.30

σσσσlong [ksi]

FPFlong [ksi] S.F. FFlong [ksi] S.F. Test 20.60 34.25 1.66 89.99 4.37Zero 13.30 34.25 2.58 89.99 6.77Work 18.20 34.25 1.88 89.99 4.94

40

Table 2.4.3 – Finite element analysis results for the initial tri-directional hybrid design incorporating hoop thickness from corrected equation.

ts = 0.155, t[±±±±20°°°°,90°°°°] = 0.184 w/ 52ksi Steel Steel σσσσVon Mises [ksi]

σσσσYield [ksi]


S.F. Test 53.30 52.00 0.98 81.00 1.52Zero 53.30 52.00 0.98 81.00 1.52Work 19.80 52.00 2.63 81.00 4.09



σσσσlong [ksi]


Table 2.5.1 – Optimized tri-directional hybrid design describing composite and steel thickness and

equivalent orthotropic elastic material properties for AS4 composite in a [±±±±20°°°°,90°°°°] lay-up.

Ex = 1.6915E+06psiEy = 1.0283E+07psiEz = 9.3876E+06psiννννxy =

5.3081E-02

ννννxz =

5.9179E-02

ννννyz =

1.5231E-01 Gxy = 6.2510E+05psiGxz = 5.8315E+05psiGyz = 2.0993E+06psit20 = 0.076in t90 = 0.129in

t[20,90] = 0.205in ts = 0.070in σσσσs =

1.00E+05psi

41

Table 2.5.2 – First Ply Failure and Fiber Failure values for the optimized tri-directional hybrid design using AS4 composite in a [±±±±20°°°°,90°°°°] lay-up.

Hoop Longitude FPF = 7.854E+04 3.932E+04 FF = 1.746E+05 1.034E+05

Table 2.5.3 – Finite element analysis results for the optimized tri-directional hybrid design.

ts = 0.07 t[±±±±20°°°°,90°°°°] = 0.205 w/ 100ksi Steel Steel σσσσVon Mises [ksi]

σσσσYield [ksi]


S.F. Test 101.00 100.00 0.99 118.00 1.17Zero 81.40 100.00 1.23 118.00 1.45Work 41.40 100.00 2.42 118.00 2.85



σσσσlong [ksi]


42

Figure 2.0.1 - Original pipe with hammer union fittings and wingnut.

43

P – Tensile Yield Stress Resultant, Νyield Qs – Stress Resultant in the Steel at Autofrettage Qc – Stress Resultant in the Composite at Autofrettage Rs – Post-Autofrettage Stress Resultant in the Steel at Zero Pressure Rc – Post-Autofrettage Stress Resultant in the Composite at Zero Pressure εQ – Strain at Autofrettage Pressure εR – Post-Autofrettage Strain at Zero Pressure εT – Strain at Fiber Failure OT – Hoop-wound CFRP OP – Elastic Range of Steel Pipe PU – Plastic Range of Steel Pipe QsRs – Post-Autofrettage Elastic Range of Steel Pipe

Qs

Rs

Rc

∆Νc2

∆εc2

εR εQ

Qc

−95

%Νyield

εεεε εT

Νyield

O

T

P

N = σσσσ t

U

Figure 2.0.2 – Stress resultant versus strain graph for the autofrettage process in the hoop direction.

44

Figure 2.1.2 – FEM with boundary conditions.Figure 2.1.1 - Steel axisymmetric model.

Restraints

Distributed Load

Longitudinal Load

Finite Elements

Fitting

Pipe

Axis of Wrapping

45

0.02.04.06.08.0

10.012.014.016.018.020.022.024.026.028.0

0 10 20 30 40 50 60 70 80 90

±θ° [degrees]

wp [l

b/ft]

Weight per Length of t(long)

Weight per Length of t(hoop)

Figure 2.2.2 – Weight per length versus lay-up angle for a bi-directional laminate.

Figure 2.2.1 – Thickness versus lay-up angle for a bi-directional laminate.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

2.20

2.40

2.60

0 10 20 30 40 50 60 70 80 90±θ ° [degrees]

t [in

]

t(long)t(hoop)

46

Figure 2.3.2 – AS4 lay-up as defined in CADEC©.

2

1

3

Figure 2.3.1 – Material coordinate systems for Microsoft® Excel and ABAQUS®.

Excel ABAQUS®

z

y

x

47

Figure 2.4.1 - Hybrid axisymmetric model.

Axis of Wrapping

Steel Liner

Composite

Fitting

Figure 2.4.2 – FEM of hybrid pipe.

Distributed Load

Gap Element

Longitudinal Load

Solid Elements

48

CP

Gap Element

Coupled DOF

Longitudinal Load

Distributed Load

Solid Element

Figure 2.4.3 – FEM of hybrid pipe showing detail of gap elements and Coupled DOF.

49

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32

tsteel [in]

t hoo

p [in

]

Case 1 (Steel Yield = 52 ksi, AS4 Composite) Case 2 (Steel Yield = 52 ksi, T800 Composite) Case 3 (Steel Yield = 100 ksi, AS4 Composite) Case 4 (Steel Yield = 100 ksi, T800 Composite)

Figure 2.5.1 – Four case comparison of steel thickness versus composite hoop thickness.

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32

Thickness of Steel [in.]

[lb/ft

]


Figure 2.5.2 – Four case comparison of steel thickness versus weight of the steel and hoop-wound composite.

50

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32

t [in]

S.F.

Case 1 (Steel Yield = 52 ksi, AS4 Composite) Case 2 (Steel Yield = 52 ksi, T800 Composite) Case 3 (Steel Yield = 100ksi, AS4 Composite) Case 4 (Steel Yield = 100 ksi, T800 Composite)

Figure 2.5.3 – Four case comparison of steel thickness versus safety factor for the hoop-wound fibers at autofrettage pressure.

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32

t [in]

S.F.


Figure 2.5.4 – Four case comparison of steel thickness versus modified safety factor for the hoop-wound fibers at autofrettage pressure.

51

Wfitting Wfitting

R

wp

Figure 2.6.1 – Pipe supported at midpoint for first beam bending scenario.

l/2 l x

V

-Wfitting

Wfitting

½ R

-½ R

Figure 2.6.2 – Shear distribution for first beam bending scenario.

Wfitting WfittingR1

wp

R2

Figure 2.6.3 – Pipe and boundary conditions for second beam bending scenario.

(Wfitting + R2) (Wfitting + R2 +¼lwp)

V

-Wfitting

-(Wfitting + ¾lwp)

¾ l l x

Figure 2.6.4 – Shear distribution for second beam bending scenario.

52

-R2 + Wfitting

R1

wp

R2

250 lbs

l/2

l x

V

125

R1 - Wfitting

Figure 2.6.5 – Pipe and boundary conditions for third beam bending scenario.

l/2

-125

Figure 2.6.6 – Shear distribution for third beam bending scenario.

53

Chapter Three

Development and Analysis

From the preliminary analyses and inspection of the design requirements, several

areas of concern were revealed in which further development of the design was required.

First, it was noticed from the analysis in 2.4 that the design had no means of transferring

the longitudinal stress component of the pressure load from the steel to the composite.

Second, it was realized that hazards exist in the work environment that could crush or

damage the pipe. Lastly, the observation was made that the pipe would undergo a torque

loading during the joining of two pipes with a threaded wing-nut. This chapter addresses

each of these issues and provides solutions to promote the success of the pipe.

3.1 Hump Design for Longitudinal Stress

All of the previously described finite element models relied on node coupling to

prevent the steel from sliding and ultimately failing beneath the composite. The design

of mechanical interlock was required for the composite to sustain the longitudinal stress.

Modifications to the steel pipe were needed. Two options were considered. The first was

to design raised pins on the surface of the steel close to the fittings. However, this design

would have left sections void of composite due to the pins separating the fiber strands.

The second option was to gradually enlarge the diameter of the pipe for a section, then

decrease the diameter in the same manner forming a hump around the pipe for the

composite to grip. This option was chosen due to ease of fabrication and pipe uniformity.

The design consisted of a hump at each end of the pipe, directly before the

fittings. During pressurization, the steel elongates and the hump acts as a wedge

underneath the composite. It was determined that two humps on each end would be

54

better than a single hump by providing an added safety factor as well as a more gradual

increase in wall thickness from the body of the pipe to the fitting, thus avoiding stress

concentrations. This design is shown in Figure 3.1.1.

An axisymmetric model of the hump design was created in I-DEAS®. The

geometry of the humps was produced using splines (smooth curves formed through

plotted points). A maximum hump thickness of 0.31 inch was chosen because it was the

thickness of the original steel pipe. The thickness of the constant cross-section region

between the outer hump and the fitting was arbitrarily chosen to be 0.2 inch.

After the hump dimensions were modeled, the composite section was created

according to the thickness requirements listed in Table 2.5.1. The model was meshed as

in previous models using 4-node axisymmetric elements. Gap elements were added

between the nodes of the steel and the composite. The hump section of the meshed

model without boundary conditions can be seen in Figure 3.1.2. Boundary conditions

and loads were defined as in previous models and the FEM was exported to ABAQUS®.

The load and material properties were edited and a solution to the model was attempted.

ABAQUS® returned errors, which indicated that the model was yielding beyond the

material definition. These errors had occurred in previous models, thus the same

temporary adjustment of the plastic material definition for the steel was used. The

ABAQUS® solver reached a solution with this modification and the results were imported

into I-DEAS® and viewed. The composite appeared to be allowing the humps to pass

under it, thereby letting the steel yield to the point of massive elongation as shown in

Figure 3.1.3. It was determined that the gap elements were not preventing the

intersection of the two materials and that the steel elements of the hump were passing

55

through the composite elements. After careful inspection of the model, the conclusion

was reached that the gap elements were not properly aligned to prevent longitudinal

translation. The node pairs separated by gap elements were aligned perpendicularly to

the longitudinal axis as shown in the hump detail of Figure 3.1.2. This prevented the

composite from expanding in the hoop direction but not along the longitudinal direction

because gap elements do not prohibit sliding. Next, to solve the problem, the humps

were partitioned into sections to facilitate alignment between the nodes of the hump and

those on the composite in an arrangement normal to the spline. The FEM was re-meshed

and Figure 3.1.4 shows the hump section and gap elements with modified alignment.

The model was exported and solved in ABAQUS® and the results were analyzed

in I-DEAS®. The new node layout provided the proper alignment for the gap elements to

prevent the two parts from sliding and intersecting. The results showed that the humps

were enabling the composite to hold onto the steel; however, stress concentrations in the

steel were found at the transitions into the first and second humps and along the 0.2 inch

thick region between the outer hump and the fitting. This excessive stress in the

transitions was due to the abrupt change from thin to thick steel and required changing

the shape of the humps to be longer with more shallow slopes. The high stress in the

section between the outer hump and fitting was due to the fact that the thickness was less

than the original 0.31 inch thickness of the all steel pipe. Since the prototype was to be

made from an existing steel pipe, the maximum thickness for the humps could not exceed

the pipe’s wall thickness. Therefore the humps were to be made by removing material on

either side of the hump area, leaving a smaller wall thickness than the original pipe,

consequently reducing the load bearing capabilities in that area.

56

It was clear that the steel between the outer hump and the fitting could not have a

smaller thickness than the original pipe. Therefore the last hump had to have a thickness

greater than 0.31 inch. A new model was created with larger humps, the inner having

0.31 inch maximum thickness and the outer hump having 0.51 inch thickness. This

model produced the desired safety factor for the steel and gave the composite an even

greater feature on which to hold. However, it presented the problem of how to attain a

steel thickness greater than that of the original pipe. A possible solution was to add weld

metal to the original pipe at the location of the large hump. A second possibility was to

fabricate custom end fittings, which include the two humps, and weld them onto a thin-

walled pipe. The second possibility was chosen but required a change in the design.

It was initially suggested that end fittings be custom made and friction-welded to

a thin-walled pipe in the same way the all-steel pipe is fabricated. This design would

cause a problem once in service because a thin weld would be required for the union

between fitting and pipe and would be the concentration point of erosion by the

transported fluids. This erosion is not a problem in the all-steel pipe due to the large wall

thickness. Therefore, the location of the weld was moved to the opposite end of the

fitting and was no longer on the surface of flow but was between the fitting and the outer

surface of the pipe. This required the pipe to pass through the humps and the fitting,

therefore all the radial dimension of the hump-fitting had to be increased to accommodate

this new “sleeve” design. Also, the humps were elongated to have smoother transitions

to help prevent stress concentrations. A diagram of this design is shown in Figure 3.1.5.

57

3.2 Material Substitution

Upon selection of FMW Rubber Products, Inc. in Bridgeport, West Virginia as

the company to filament wind the prototype, the design and materials were discussed. It

was discovered that the original carbon fiber AS4, chosen at the onset of this project was

more costly than expected. After investigation of alternate choices, a generic carbon

fiber, TR50, was chosen because of its material properties and reduced cost. Its fiber

elastic modulus was comparable to that of AS4 while its ultimate strength was greater

than AS4. EPON 828 epoxy resin cured with EPI-CURE 3140 Polymide Curing Agent

[25] was the chosen resin as recommended by FMW due to positive experiences with the

product. The known properties of TR50 and EPON 828 with EPI-CURE 3140 are shown

in Table 3.2.1.

The material properties for a composite of TR50 and EPON 828 were unknown.

The standard methods for determining these properties are through experimental testing,

which is costly and time consuming. An alternative to experimental analysis would be to

numerically calculate the material properties from the known properties of the fiber and

resin, which were provided by the manufacturers. CADEC© was used to perform the

calculations but some of the required values were not known and were taken from the

properties of AS4/3501-6 [22]. Table 3.2.2 shows the properties and values, which were

input into CADEC©. The transversely isotropic elastic material properties for a

unidirectional composite of TR50/EPON 828 were computed and are shown in Table

3.2.3.

The question of what yield strength to use in the prototype became more

important as the project continued. Up to this point, all analyses were performed using

58

the properties of 4130 as chosen from Mechanical Engineering Design 5th Edition [21].

When the question was posed to Halliburton, two steel options were given in reply. The

pipe could be heat treated to have a yield strength of 93 ksi or 120 ksi, so a comparative

analysis was necessary to make a final choice.

3.3 Analysis of the Sleeve Design

The properties of TR50/EPON 828, 93 ksi steel and 120 ksi steel were input into

Excel spreadsheet TR50_with_93ksi_&_120ksi.xls to determine the required composite

thickness of the hoop and longitudinal layers according to the thickness range of steel.

Figure 3.3.1 is a graph of the factor of safety for the hoop loading versus the steel

thickness for the two scenarios and Figure 3.3.2 is the weight of the steel and hoop-

wound composite plotted against the steel thickness. It was recommended to and

accepted by Halliburton that the 120 ksi steel be used for the prototypes due to the

reduced design weight compared to the 93 ksi steel. After considering the safety factor

graph, a steel liner was chosen by Halliburton with a 0.065 inch wall thickness and 1.995

inch inner diameter. The thickness and equivalent elastic material properties of the [±20º,

90º] composite with 0.065 inch steel are shown in Table 3.3.1, the orthotropic properties

were converted into the ABAQUS® coordinate system as described in the previous

chapter. The FPF and FF values of the composite for the hoop and longitudinal

directions with a 17% knockdown due to filament winding are shown in Table 3.3.2.

Previous analyses did not include such a strength reduction.

The sleeve design was modeled and analyzed using I-DEAS® and ABAQUS®

respectively. The FEM consisted of three parts: the steel pipe liner, the hump/fitting

sleeve and the composite as shown in the exploded diagram of Figure 3.3.3. A change in

59

element selection was made, to 8-node axisymmetric elements, instead of the 4-node

elements of previous models, to generate a more accurate representation of the actual

pipe. Figure 3.3.4 shows the FEM after the nodes and elements were meshed. The parts

were separated from one another by 0.005” gaps. Gap elements were used to define the

contact between the liner and sleeve, the liner and composite, and the sleeve and

composite. The assembly was restrained and loaded with an internal pressure, as

previously described.

The model was exported, modified, solved in ABAQUS®, and imported back into

I-DEAS®. The results in the steel and composite taken along the constant thickness

section show that the steel yields and is compressed to 74% of yield after autofrettage, as

shown in Table 3.3.3. The results in the composite over the humps showed that the

composite was near failure and was in need of reinforcement along that region to prevent

the humps from moving.

A layer of hoop-wound composite, 0.125 inch thick, was added overtop of the

[±20°, 90°] base composite on the humps as shown in the exploded diagram in Figure

3.3.5. The equivalent orthotropic material properties of the reinforcement is shown in

Table 3.3.4. Coupled degrees of freedom were used to join the [90°] reinforcing

composite to the [±20°, 90°] base. The material properties of the composite elements

were defined to be orthotropic and were divided into two groups: base composite

material, COMP2090, and the reinforcement material, COMP90. When analyzed, this

design produced the same results in the constant thickness section as in Table 3.3.3, but

displayed maximum stresses (Von Mises, hoop and longitudinal) throughout the entire

model as shown in Table 3.3.5. It can be seen from this table that stress concentrations,

60

near the steel ultimate stress, exist in the hump/fitting and the liner. It was determined

that these concentrations were at a location that would not affect the success of the pipe.

It was also realized that the 120 ksi yield strength for the steel might not be

accurate. A sensitivity analysis was performed to determine the effects of a ±5% change

in the yield strength of the steel for the design based on 120 ksi yield strength. The same

FEM from the analysis above was used and only required the modification of the plastic

material definition of the steel. For the first case the material was defined with a yield

strength of 114 ksi and an ultimate strength of 119 ksi. The model was solved in

ABAQUS®, viewed in I-DEAS® and the results are recorded in Table 3.3.6. It can be

seen that the liner is autofrettaged but is within 84.7% of compressive yield, which is

greater than the same design with 120 ksi steel. The safety factors in the composite are

reduced but not drastically.

For the final case the material was defined with a yield strength of 126 ksi and an

ultimate strength of 132 ksi. The model was solved in ABAQUS®, viewed in I-DEAS®

and the results are recorded in Table 3.3.7. It can be seen that the liner is autofrettaged

but is within 63.6% of compressive yield, which is less than the same design with 120 ksi

steel. The safety factors in the composite show a slight increase over those in Table

3.3.3.

The sleeve design proved to be a good method for transferring the longitudinal

load from the fitting to the composite and alleviating the longitudinal stress in the liner.

It was also concluded from the sensitivity analysis that a ±5% change in the yield

strength of the steel will mainly affect the amount of autofrettage but was deemed as

61

acceptable tolerances. Diagrams of the sleeve with dimensions are found in Figures 3.3.6

through 3.3.10.

3.4 Ovalization Analysis

It was determined that in the rugged work environment of the petroleum industry,

the pipe could undergo unique stress situations for which it was not designed. One

possible scenerio would be for a load to be applied in such a way that might crush or

ovalize the pipe. This situation could occur if the pipe were to be run over by a vehicle.

A finite element analysis was performed using SDRC® I-DEAS® to simulate a heavy

truck resting one tire upon the pipe positioned horizontally on the ground.

The pipe was modeled as two tubes, one inside the other separated by a 0.005

inch gap. To save solution time, the pipe was cut in half longitudinally as seen in Figure

3.4.1. The model was meshed with 8-node block shaped elements. The material

properties of generic isotropic steel were assigned to the elements of the inner tube and

the orthotropic elastic material properties from Table 3.3.1 were assigned to the elements

of the outer tube. Since the model is cylindrical the composite’s orthotropic properties

change around the pipe. The global coordinate system in I-DEAS® is Cartesian, so a

second system using cylindrical coordinates was created for the composite elements to

reference thus allowing proper material alignment.

Due to the amount of finite elements in the model, the gap elements used in

previous models were impractical. Instead, a contact set was created. This is a means of

defining contact between elements of one part with the elements of another part by

specifying a maximum gap distance for which the program would search. When the

62

program finds two elements with a gap between them less than or equal to the maximum

gap distance, a contact is defined between them thus preventing intersection.

The model was loaded by applying concentrated forces to the nodes in the shaded

area of Figure 3.4.2. The area covers 12 inches along the longitude of the pipe and 0.81

inch in width. Forces were applied to seven rows of nodes, 111 in each row for a total of

777 forces. Figure 3.4.3 shows the cross-sectional view of the mesh with 7 rows of

forces. Each force in the three left-most rows was equal to 4 lbs, the next two rows were

made up of 3 lb forces and the remaining two right-most rows consisted of 2 lb forces.

The sum total of the 777 forces was equal to 2442 lbs. This represents the tire load of an

equipment truck used by Halliburton Company.

The nodes located on planar surfaces were restrained with symmetric boundary

conditions as follows:

1) Nodes on planar surfaces parallel to the xy-plane were restrained from having

z-translation, x-rotation and y-rotation.

2) Nodes on planar surfaces parallel to the yz-plane were restrained from having

x-translation, y-rotation and z-rotation.

The model was solved and the maximum Von Mises stress in the steel was

recorded but the stresses in the composite could only be recorded in three areas.

I-DEAS® displays stress components along the x, y and z axes, but the composite

material follows a cylindrical coordinate system so the results were recorded only for the

three groups of elements shown in Figure 3.4.4. These results are displayed in Table

3.4.1. It was concluded that the pipe could withstand the ovalization loading with a

minimum safety factor of 5.49.

63

3.5 Track Design for Torsion Load

It was realized that the Weco 1502 hammer unions used to join two pipes would

create a torque load in the pipe. This would be negligible in the original steel pipe but

would cause problems for the hybrid design. These unions consist of a wing-nut joining

a threaded female fitting on one pipe to a male fitting on another pipe, as shown in Figure

2.0.1. The nut is hand tightened and then struck repeatedly on the wings with a 5 lb

hammer until a ringing sound is heard, signifying metal-to-metal contact. The hammer’s

striking point is approximately 4.5 inches from the center of the pipe, which can cause a

considerable amount of torque depending on the person swinging the hammer. The

existing design had no physical provision for torque loading and would result in buckling

failure in the thin-walled steel beneath the composite.

It was determined that the hump closest to the fitting would be machined in such a

way so that the fiber could grip the steel and allow torque to transfer from the steel to the

composite. A track design was chosen which consisted of four hourglass shaped tracks

milled through the hump, as shown in the unwrapped drawing in Figure 3.5.1 and the

cross-sectional view in Figure 3.5.2. The geometry of the tracks was designed based on

the lay-up angle and cross-sectional area of the ±20° fibers. It was decided that the

narrow section, the bottleneck, of the hourglass would be located at the thickest point of

the hump and the cross-sectional area of the four tracks at the bottleneck must equal the

total cross-sectional area of the ±20° fibers, Ac from (2.2.42), as in the following equation

c trackA NA= (3.5.1)

where N is the number of tracks and Atrack is the cross-sectional area at the bottleneck of

one track, calculated by

64

( )2 22 1 360trackA r r θπ= − (3.5.2)

where r1 and r2 are the radii of the bottom and top of the track respectively and θ is the

angle between the walls of the track. Figure 3.5.3 describes r1, r2 and θ. The value for r2

was known because it is the radius of the top of the large hump. The value of r1 was

determined trigonometrically from Figure 3.5.4 and the angle θ was found by combining

(3.5.1) and (3.5.2) to get

( )2 22 1

360 cAN r r

θπ

=−

(3.5.3)

Using θ, the arc lengths at the top and bottom of the bottleneck, a1 and a2 respectively,

were calculated with

2360

ra π θ= (3.5.4)

During filament winding, the ±20° fibers would fill the tracks and be covered by

90° reinforcing fibers. As the wing-nut is tightened, the load would be transferred

through the walls into the composite. Two analyses of this modified design were

performed to determine the stress on the composite in the track section and the maximum

allowable force and hammer velocity that could be applied to the wing-nut.

3.6 Simplified Torque Analysis

The composite was analyzed to determine the maximum impact force that could

be applied to the wing-nut. The composite over-wrap was analyzed by itself because it

was desired that the steel bear as little of the stress as possible.

The polar moment of inertia of the composite was calculated by

( ) ( )( )4 42 2 232

J r t rπ= + − (3.6.1)

65

where r is the inner radius of the composite and t is its thickness. The equation for

torsional stress is

( )T r tJ

τ += (3.6.2)

where T is the applied torque which is represented by

wingT r F= (3.6.3)

with rwing as the radius of the striking point of the hammer on the wing-nut and F is the

force applied to the wing-nut. By combining (3.6.2) with (3.6.3) and replacing τ with the

ultimate in-plane shear strength of the laminate, FFshear(with 17% knockdown for

filament winding), the maximum force was calculated as

( )shear

FFwing

FF JFr r t

=+

(3.6.4)

and is reported in Table 3.6.1. This table also shows the torque, TFF, at shear failure

calculated using (3.6.3).

Since this is an impact loading, the impact velocity of the hammer was calculated

according to the maximum force. The strain energy of the composite, U, and the kinetic

energy of the hammer, UH, must satisfy the principle of conservation of energy as shown

HU U= (3.6.5)

The strain energy equation is

2

2 yz

T lUG J

= (3.6.6)

where l is the length of the pipe and Gyz is the in-plane shear modulus of the composite.

The kinetic energy of the hammer is

212H H HU m v= (3.6.7)

66

where vH is the velocity of the hammer and mH is its mass calculated as

HH

Wmg

= (3.6.8)

where WH is its weight and g is the gravitational constant equal to 32.2 ft/s2. The

maximum hammer velocity was determined by rearranging equations (3.6.5) through

(3.6.7) to get

( )22

wing FFH

HH yzyz

r F lT lvWm G J G J

g

= = (3.6.9)

The values of FFshear, FFF, TFF and νH are recorded in Table 3.6.1. It is concluded from

this analysis that the wing-nut cannot be tightened with an impact velocity greater than

7.76 ft/sec when using a 5 lb hammer.

3.7 Finite Element Analysis of the Track Design

The complexity of the track design required the use of FEA. SDRC® I-DEAS®

was used to create a three-dimensional model of the hump section. In an effort to reduce

the computing time, the fitting and thin-walled steel pipe was not modeled.

The geometry of the humps was created by revolving a two-dimensional cross-

section that resembled the axisymmetric model but displayed a flat region in place of the

large hump, Figure 3.7.1. This produced a part with one hump and a smooth tapered

section for the base of the large hump/tracks, Figure 3.7.2. The tracks were designed to

be four hourglass shaped channels through the humps, which would leave four raised

diamond shapes at the former location of the large hump. The diamonds were formed by

revolving a hump shaped cross-section and then cutting away four hourglass shaped

tracks. The diamonds are shown in Figure 3.7.3. These diamonds were then joined to

67

the steel hump section to produce the part found in Figure 3.7.4. The part was meshed

with 8-node block shaped solid elements and is shown in Figure 3.7.5. The material

properties of the elements were consistent with generic isotropic steel without plastic

properties defined.

The composite was modeled in the same manner as the steel hump section. First,

a longitudinal cross-section of the [±20°, 90°] base with the [90°] reinforcement was

modeled and is shown in Figure 3.7.6. This part was revolved to form the solid model in

Figure 3.7.7. The composite was now formed but lacked the internal geometry to

interlock with the hourglass shaped tracks of the steel hump. A copy of the four diamond

shaped track forms was used to cut the composite. An interior view of the composite

with cutouts is shown in Figure 3.7.8. The composite model was meshed and is shown in

Figure 3.7.9. Material properties were created for three orthotropic materials, the

[±20°,90°] base composite, [90°] reinforcing composite and the [±20°] composite in the

tracks. A cylindrical coordinate system was created and the three composite materials

were then aligned to it in the same way as in the ovalization model.

The two meshes, steel and composite, were appended into one FEM and boundary

conditions were created. In order to prevent the steel elements from intersecting the

composite, contact had to be defined. Due to the complexity and massive amount of

finite elements in the model, a contact set was used as described earlier. The composite

elements at the end closest to the small hump were restrained from having any

translation. The torque was to be applied to the steel elements at the opposite end of the

model, but to apply the load uniformly it was required to be on the longitudinal axis of

the pipe. Since loads must be applied on nodes or elements, a modification to the steel

68

mesh was needed. A node was created on the longitudinal axis at the fitting end of the

model and 2-node rigid bar elements were created between this node and the nodes of the

steel mesh as shown in Figure 3.7.10. Since the simplified torque analysis predicted a

maximum torque of 4437 in-lbs, an axial torque of 5000 in-lbs was applied to the node,

as shown in the figure, and the rigid elements transferred the load from the center node to

the steel.

A solution to the model was attempted but was unreachable because of the

number of elements, contact definition and complexity of the analysis. So the model was

simplified to facilitate a solution. The small hump and composite covering the small

hump was removed and the straight region between the hump/tracks and the fitting end

was shortened. The steel part of this model is shown in Figure 3.7.11. A solution was

reached and the stresses in the composite are recorded in Table 3.7.1. It is shown that the

safety factor in the base composite was 1.03 at 5000 in-lbs of torque. This reinforces the

simplified torque analysis, which calculated the maximum allowable torque to be 4437

in-lbs. It is also noticed that the safety factor in the ±20° track composite was 2.64 at

5000 in-lbs, which relieves concerns of failure in the track region due to torque loading.

These results proved that the track design is a valid method for transferring the torque

load from the fitting to the composite.

3.8 Conclusions

From the research and analysis recorded in this chapter it was concluded that:

• The steel pipe between the last hump and the fitting must be as thick as the original

steel pipe because the composite in that region does not help carry longitudinal stress.

69

• Gap elements must be aligned normal to the contour of the edge of contact to prevent

intersection of the parts.

• The sleeve design was chosen to avoid a weld where it may be eroded/corroded.

• CADEC© was used to predict properties of composites based on fiber and resin

properties.

• Care must be taken when writing the coordinate system for the material properties

and when converting the material coordinate system to the global system of I-DEAS®

and ABAQUS®.

• The sensitivity analysis showed that ±5% difference in the yield strength of the steel

is acceptable, but a greater tolerance is not recommended because it compromises the

compressive stress limit at zero pressure.

• The ovalization analysis proved that the pipe can withstand extremely large crush

loads from workplace hazards.

• The track design proved to be an effective method for transferring the torque applied

during the joining of two pipes.

• The simplified torque analysis predicted that the base composite could withstand the

torque produced by a hammer striking the wing-nut with a maximum velocity of 7.76

ft/sec.

• The FEA of the track design predicted that the base composite would fail before the

±20° composite in the tracks. It also reinforced the results from the simplified torque

analysis.

70

Table 3.2.1 – Known properties of TR50 carbon fiber and EPON 828 epoxy.

Table 3.2.2 – Properties used in CADEC© to determine transversely isotropic material properties for

a unidirectional composite of TR50/EPON 828.

Fiber Properties Resin PropertiesEf = 3.45E+07 Em = 3.20E+05 ννννf = 0.22 ννννm

= 0.38 ααααf = 5.40E-06 ααααm

= 3.00E-05 kf = 1.05 km = 0.20 Vf = 0.60 ρρρρm

= 1.20 a/b = 1.00 ββββm

= 0.60 ρρρρfa

= 0.066 Vv = 0.02 σσσσfa

= 5.26E+05 σσσσmu

= 7.30E+03 ΩΩΩΩ

= 3.53 σσσσmuc

= 3.40E+04 ττττmu

= 3.65E+03

Fiber Properties Fiber Tensile Modulus, [psi] = 34500000 Fiber Tensile Ultimate Strength, [psi] = 526000

Resin Properties Heat Deflection Temperature, [C] = 72 Ultimate Tensile Strength, [psi] = 7300 Tensile Elongation, [%] = 11.8 Initial Tensile Modulus, [psi] = 320000 Ultimate Flexural Strength, [psi] = 12000 Flexural Deflection, [in] = 0.6 Initial Flexural Modulus, [psi] = 340000 Ultimate Compression Stregth [psi] = 34000 Compression Yield Strength, [psi] = 9100 Izod Impact, [ft-lb/inch notch] = 0.88 Hardness, Shore D = 82 Water Absorption = 0.33 Weight Loss = 0.05 Dielectric Constant = 3.41 Dissipation Factor = 0.018

71

Table 3.2.3 – Transversely isotropic elastic material properties for a unidirectional composite of TR50/EPON 828 produced in CADEC©.

Properties E1 = 2.08E+07E2 = 1.67E+06G12 = 4.50E+05G23 = 3.98E+05νννν12

= 0.284 νννν23

= 0.573

Table 3.3.1 – Sleeve design describing composite thickness, liner thickness and equivalent orthotropic elastic material properties for TR50 composite in a [±±±±20°°°°,90°°°°] lay-up.

Ex = 2.26E+06psiEy = 7.83E+06psiEz = 1.27E+07psiννννxy =

1.39E-01 ννννxz =

7.27E-02 ννννyz =

1.03E-01 Gxy = 4.17E+05psiGxz = 4.31E+05psiGyz = 1.31E+06psit20 = 0.0602 in t90 = 0.0834 in

ttotal = 0.1436 in ts = 0.065 in

IDs = 1.995 in σσσσs =

1.20E+05psi

72

Table 3.3.2 – First Ply Failure and Fiber Failure values for the sleeve design using TR50 composite in a [±±±±20°°°°,90°°°°] lay-up.

Hoop Hoop w/ 17% Knockdown Longitude Long w/ 17% KnockdownFPF [psi] = 3.525E+04 2.926E+04 1.954E+04 1.622E+04 FF [psi] = 1.931E+05 1.603E+05 1.356E+05 1.126E+05

Table 3.3.3 – Finite element analysis results in steel and composite along the section of constant thickness, away from the hump/fitting.

ts = .065 t[±20°,90°] = .1436 w/ 120ksi Steel Liner σσσσVon Mises [ksi]

σσσσYield [ksi]


S.F. Test 120 120 1.00 126 1.05 Zero 88.4 120 1.36 126 1.43 Work 64.2 120 1.87 126 1.96

[±±±±20°°°°,90°°°°] σσσσhoop [ksi]

FPFhoop [ksi] S.F. FFhoop [ksi] S.F. Test 117 29.26 0.25 160.28 1.37 Zero 45.1 29.26 0.65 160.28 3.55 Work 93.3 29.26 0.31 160.28 1.72

σσσσlong [ksi]

FPFlong [ksi] S.F. FFlong [ksi] S.F. Test 35.2 16.22 0.46 112.57 3.20 Zero 12 16.22 1.35 112.57 9.38 Work 27.6 16.22 0.59 112.57 4.08

Table 3.3.4 – Equivalent orthotropic elastic material properties for TR50 composite in a [90°°°°] lay-up.

Ex = 1.665E+06 psiEy = 1.665E+06 psiEz = 2.082E+07 psiννννxy =

5.73E-01 ννννxz =

2.27E-02 ννννyz =

2.27E-02 Gxy = 3.976E+05 psiGxz = 4.499E+05 psiGyz = 4.499E+05 psi

73

Table 3.3.5 – Maximum stress values from the FEM of the sleeve with reinforcement.


σσσσYield [ksi]


S.F. Test 124.80 120.00 0.96 126.78 1.02 Zero 106.50 120.00 1.13 126.78 1.19 Work 90.20 120.00 1.33 126.78 1.41 Burst 129.70 120.00 0.93 126.78 0.98

Humps σσσσVon Mises [ksi]

σσσσYield [ksi]



[±±±±20°°°°,90°°°°] σσσσhoop [ksi]

FPFhoop [ksi] S.F. FFhoop [ksi] S.F. Test 118.10 29.26 0.25 160.28 1.36 Zero 45.60 29.26 0.64 160.28 3.51 Work 94.00 29.26 0.31 160.28 1.71 Burst 184.20 29.26 0.16 160.28 0.87

σσσσlong [ksi]

FPFlong [ksi] S.F. FFlong [ksi] S.F. Test 53.60 16.22 0.30 112.57 2.10 Zero 21.50 16.22 0.75 112.57 5.24 Work 43.00 16.22 0.38 112.57 2.62 Burst 96.30 16.22 0.17 112.57 1.17

[90°°°°] σσσσhoop [ksi]


σσσσlong [ksi]

FPFlong [ksi] S.F. FFlong [ksi] S.F. Test 17.50 3.69 0.21 - - Zero 8.50 3.69 0.43 - - Work 14.40 3.69 0.26 - - Burst 33.20 3.69 0.11 - -

74

Table 3.3.6 – Sensitivity FEA results from the section of constant thickness using 114 ksi yield strength steel.


σσσσYield [ksi]


S.F. Test 114.35 114.00 1.00 119.00 1.04 Zero 96.59 114.00 1.18 119.00 1.23 Work 58.37 114.00 1.95 119.00 2.04

[±±±±20°°°°,90°°°°] σσσσhoop [ksi]

FPFhoop [ksi] S.F. FFhoop [ksi] S.F. Test 120.50 30.67 0.25 168.00 1.39 Zero 49.87 30.67 0.61 168.00 3.37 Work 97.00 30.67 0.32 168.00 1.73

σσσσlong [ksi]

FPFlong [ksi] S.F. FFlong [ksi] S.F. Test 37.33 17.00 0.46 117.97 3.16 Zero 13.77 17.00 1.23 117.97 8.57 Work 29.66 17.00 0.57 117.97 3.98

Table 3.3.7 – Sensitivity FEA results from the section of constant thickness using 126 ksi yield strength steel.


σσσσYield [ksi]


S.F. Test 126.30 126.00 1.00 132.00 1.05 Zero 80.16 126.00 1.57 132.00 1.65 Work 66.89 126.00 1.88 132.00 1.97

[±±±±20°°°°,90°°°°] σσσσhoop [ksi]

FPFhoop [ksi] S.F. FFhoop [ksi] S.F. Test 111.20 30.67 0.28 168.00 1.51 Zero 40.88 30.67 0.75 168.00 4.11 Work 87.76 30.67 0.35 168.00 1.91

σσσσlong [ksi]

FPFlong [ksi] S.F. FFlong [ksi] S.F. Test 37.64 17.00 0.45 117.97 3.13 Zero 15.25 17.00 1.11 117.97 7.74 Work 30.18 17.00 0.56 117.97 3.91

75

Table 3.4.1 – Results from ovalization analysis showing the maximum stresses and safety factors at fiber failure for the steel and the three groups of composite elements.

Table 3.6.1 – Values of FFshear, FFF and ννννH for the simplified torque analysis.

FFshear [psi] = 4850 FFshear [psi] w/ 17% knockdown= 4025 FFF [lbs] = 986 TFF [in-lbs] = 4437 vH [in/sec] = 93 vH [ft/sec] = 7.76

Table 3.7.1 – Results from the torque analysis describing the maximum shear stresses, fiber failure values and safety factors for the [±±±±20°°°°,90°°°°] base composite and the [±±±±20°°°°] composite in the tracks.

[±±±±20°°°°,90°°°°] Base ττττmax [psi]

= 3920FFshear [psi] = 4025S.F. = 1.03

[±±±±20°°°°] Tracks ττττmax [psi]

= 2910FFshear [psi] = 7689S.F. = 2.64

Liner σσσσVon Mises [psi]

= 17200S.F. = 6.98

[±±±±20°°°°,90°°°°] Group #1 σσσσhoop [psi]

= -18900S.F. = 8.47

σσσσlong [psi]

= 20400S.F. = 5.49


= -17500S.F. = 9.14

σσσσlong [psi]

= 7180 S.F. = 15.60


= -13500S.F. = 11.85

σσσσlong [psi]

= 7780 S.F. = 14.40

76

Figure 3.1.1 – Initial hump design for longitudinal stress.

Figure 3.1.2 – FEM of initial hump design showing detail of gap elements on lower hump.

Figure 3.1.3 – Stress contour for initial hump design showing massive elongation and

intersection of steel and composite.

Intersection of steel and composite

Gap Elements Aligned Perpendicular to Longitudinal Axis

77

Gap Elements Aligned Normal

to the contour of the hump

Figure 3.1.4 – Meshed hump section showing detail of gap elements aligned normal to the spline curve of the hump.

Figure 3.1.5 – Sleeve design without composite over-wrap.

78

Figure 3.3.1 – Two case comparison of steel thickness versus modified safety factor for the hoop-wound fibers at autofrettage pressure.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32

t [in]

S.F.

Case 1 (Steel Yield = 93 ksi)


0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

8.0

8.5

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32

Thickness of Steel [in.]

[lb/ft

]

Case 1 (Steel Yield =93 ksi)


Figure 3.3.2 – Two case comparison of steel thickness versus weight of the steel and hoop-wound composite.

79

Figure 3.3.3 – Exploded view of sleeve model showing the three parts.

Figure 3.3.4 – Meshed finite element model of the sleeve design.

Hump/Fitting Sleeve

Liner

Composite

80

Figure 3.3.5 – Exploded view of sleeve model with reinforcement over the humps.

[90º] Reinforcing Composite

[±20º, 90º] Base Composite

Hump/Fitting Sleeve

Liner

81

Figure 3.3.6 – Diametric dimensions of the hump/fitting for the sleeve design.

Figure 3.3.8 – Longitudinal dimensions of the hump/fitting for the sleeve design.

Figure 3.3.7 – Thickness dimensions of the hump/fitting for the sleeve design.

82

Figure 3.3.9 – Angular dimensions of the hump/fitting for the sleeve design.

Figure 3.3.10 – Radial dimensions of the hump/fitting for the sleeve design.

83

Figure 3.4.1 – Cross-sectional and three-dimensional views of the model used for the ovalization analysis.

Cross-Sectional View

Composite

Steel Liner

84

Figure 3.4.2 – Three-dimensional view of the model with shaded area describing load location.

85

Figure 3.4.3 – Cross-sectional view of the model with arrows depicting seven rows of nodal forces.

Three Rows of 4 lb Forces

Two Rows of 2 lb Forces

Two Rows of 3 lb Forces

86

Figure 3.4.4 – Cross-sectional and three-dimensional views of composite elements from which results were taken.

Cross-Sectional View

Group #1

Group #3

Group #2

87

Figure 3.5.1 – Unwrapped view of the large hump showing dimensions of the track design.

Figure 3.5.2 – Dimensions of the track design in a cross-sectional view.

88

Figure 3.5.3 – Variable dimensions used to determine the track design.

r2 r1

θ

a1

a2

Figure 3.5.4 – Diagram used to determine the radius of the track bottom at the bottleneck of the track design.

r1r2 =

89

Figure 3.7.1 – Longitudinal cross-section of steel hump section without large hump.

Figure 3.7.2 – Solid model of steel hump section without large hump.

90

Figure 3.7.3 – Solid model of the four steel diamond shaped track forms.

91

Figure 3.7.4 – Solid model of the completed steel hump section with tracks.

Figure 3.7.5 – Meshed FEM of the steel hump section with tracks.

92

Figure 3.7.6 – Longitudinal cross-section of composite section including reinforcement.

Figure 3.7.7 – Solid model of composite section including reinforcement.

93

Figure 3.7.9 – Meshed FEM of the composite part.

Figure 3.7.8 – Interior view of the composite showing diamond shaped cutouts.

94

Figure 3.7.10 – End of steel mesh showing node, rigid bar elements and applied torque load.

Steel Elements

Torque

Rigid Elements

Node

∗

95

Figure 3.7.11 – Steel part of the simplified model for the torque analysis.

96

Chapter Four

Fabrication and Testing

4.1 Fabrication

Upon completion of the design and analyses, shop drawings for the fabrication of

the steel liner and fittings were submitted to Stan Stephenson at Halliburton Company.

The hump/track fittings were machined from 4130 steel and were positioned and welded

at the ends of the 10 foot liner, which was also made of 4130 steel. Residual stresses

were introduced into the steel through the welding process requiring a heat treatment for

relief. A furnace stress relieve at 900 F was performed for one hour on each end of the

pipe. The temperature was verified with the use of a thermocouple and the time was

monitored. After the pipes cooled, Loctite 290 was introduced into the gap between the

hump/track sleeve and the liner to seal and protect the pipe from internal corrosion and

rust.

Four steel prototypes were produced and delivered to FMW Rubber Products, Inc.

in Bridgeport, West Virginia. Composite design specifications were given to Don Mott

at FMW and one prototype was prepared and fabricated as described below.

The pipe was cleaned, degreased and coated with a paint-on insulation, Siloxirane

#32 with Catalyst #32 from Advanced Polymer Coatings, to prevent galvanic corrosion

between the steel liner and the carbon fibers. The computer-controlled filament-winding

machine was prepared and the ends of the mandrel were inserted into the mounting

chucks. The placement of the fibers was controlled by the computer as the pipe rotated.

The first layer was ±20º followed by a 90º layer and alternated in this manner until the

total required thickness for the two layer orientations were fulfilled. The ±20º fibers were

97

wound and allowed to pass over the inner humps and through the tracks on the outer

humps at which point they were turned around for a pass in the opposite direction. The

90º fibers were wound only over the body of the pipe and the inner humps. They were

not allowed on the outer humps because this would block the tracks and not allow the

±20º fibers to be placed properly. As the fibers were placed on the rotating pipe, the

operator distributed and removed excess resin by dragging a wide, flat, flexible piece of

plastic along the composite thereby spreading and extracting the extra epoxy. During

placement of the ±20º fibers through the tracks, it was noticed that there were four

triangular shaped areas, between the mouth of each track and the turnaround space, that

were absent of fibers. Figure 4.1 shows the area void of composite. It was determined

that due to the angle of the fibers exiting the tracks, that area could not be covered and

would leave a void space underneath the 90º reinforcement composite. It was also

noticed that the fibers did not always fall nicely into the tracks and required manual

adjustment by the operator, sometime involving halting the winder and reversing the

rotation to unwind that section. A suggestion was made for future pipes to have raised

triangular shaped guides welded or bonded to the void region to aid in automating the

placement of fibers into and exiting the track at the turnaround area.

Diametric measurements were taken upon completion of each layer to gage and

adjust the computer program for accuracy and to assure a fiber volume fraction of 60%

by volume. After all layers were complete, additional 90º fibers were wound over the

outer track/humps to restrain the underlying fibers. The 0.125 inch 90º reinforcing layer

was then wound over both sets of humps.

98

The process experienced downtime for mechanical problems and break periods

for the operators. After such interludes, the resin began to harden and required the

introduction of heat from a hand held heat gun, essentially to melt the epoxy and promote

bonding of new layers.

After all the layers of the carbon/epoxy were completed, a protective layer of

glass fiber was added using the same resin. The pipe was finished without a soft impact

resistant layer of padding, as more research was needed to determine the best material for

impact protection.

The weights of the mandrel, steel liner, composite and completed hybrid pipe are

shown in Table 4.1. The hybrid pipe yields a 29.5% weight reduction when compared to

the original all-steel pipe, which weighs 105 lbs. The pipe was shipped to Halliburton

Co. in Duncan, Oklahoma for testing. The remaining three pipes, at the completion of

this research, were stored at FMW ready for fabrication according to current and future

design changes.

4.2 Testing

The pipe was tested at Halliburton Company. The pipe was installed in the test

chamber by tightening the wing-nuts with a sledge hammer. The pipe was visually

inspected for signs of composite damage due to the torque applied during mounting, but

neither micro-cracks nor fiber breakage was found. The prototype was slowly

pressurized with water to the autofrettage load of 22.5 ksi and held for one minute before

unloading. After the load was removed, the pipe was disconnected from the test fixture

and visually inspected. It was noticed that the interior of the pipe had no visible defects

such as bulges or kinks and the exterior showed no signs of damaged fibers or micro-

99

cracks in the resin. The pipe was reconnected and slowly loaded to 29.4 ksi at which

point catastrophic failure occurred. According to Table 3.3.3, the safety factor in the

hoop direction of the base composite was 1.36 at 22.5 ksi, therefore the predicted pipe

failure was to be at 30.8 ksi which proved to be a good representation of the actual test.

However, metal pipes typically fail by splitting along its longitude, which is an

acceptable failure mode. The prototype failed by breaking into three separate parts. It

appears that it first started to split along the longitude but after the crack lengthened

beyond 6 inches, it was unable to continue and both ends of the crack changed direction

and progressed hoop-wise around the pipe, thus resulting in a short section breaking free

of the two end sections. This outcome was not expected due to the safety factors

presented in Table 3.3.3 and Table 3.3.5. The theoretical results from the region of

constant thickness, where the rupture occurred, revealed that the longitudinal safety

factor of the base composite at autofrettage was about 2.34 times greater than the safety

factor in the hoop direction. It is believed that the discrepancy was due to the fact that

the FF values from CADEC were based on unidirectional loading conditions. This is

acceptable for the 90º component of the base composite because it focuses nearly its

entire strength in the hoop direction. But the ±20º fibers have the ability to bear stress in

the hoop and longitudinal directions. Since the longitudinal component was analyzed

with only the longitudinal FF stress in mind, the added stress from the combined loading

proved to be too much. The mode of failure was deemed unacceptable and modifications

to the design were required.

100

Table 4.1 – Individual component and combined weights of the hybrid pipe.

Description Weight [lbs.] Mandrel 89

Steel Liner with Fittings and Wing-Nut 57

Composite 17 Completed Pipe 74

101

Figure 4.1 – Hump/tracks showing ±20ºcarbon fibers and the triangular shaped void.

Triangular Void

Carbon Fibers

102

Chapter Five

Design Modification

From the failure mode of the prototype, it was determined that the design of the

[±20°] component of the base composite must be modified to produce the desired

longitudinal splitting during pipe failure. A hybrid composite consisting of TR50 hoop-

wound fibers and Kevlar® 49 longitudinal fibers was analyzed for the redesigned base

composite. Kevlar® 49 was chosen due to its high elongation to failure and its fiber

ultimate strength, which matches that of TR50. These properties and the elastic modulus

of each fiber are listed in Table 5.1. Table 5.2 shows the elastic properties of TR50 and

Kevlar® 49 in separate unidirectional composites with epoxy resin EPON 828.

An Excel spreadsheet, kevlar_carbon.xls, was created using the same methods

and equations as previous spreadsheets but was modified so that equations related to the

[±20°] portion of the composite relied on the material properties of Kevlar® 49. As in

previous spreadsheets, this one produced the equivalent orthotropic material properties

and thickness for the base material to be modeled and analyzed using I-DEAS® and

ABAQUS® respectively. These values are shown in Table 5.3.

The design was modeled in much the same way as earlier models but a change

was made concerning the reinforcing composite. The hoop-wound reinforcement in

previous models was joined to the base composite using Coupled DOF, but for all the

analyses performed for the redesigned prototype the reinforcement and the base were

modeled together as one part without a gap. This part was partitioned using the

procedure listed in Appendix A according to the prescribed thickness of each material.

An exploded diagram of the model is shown in Figure 5.1.

103

The model was meshed, restrained, loaded and exported to ABAQUS®. The load

steps and material definitions were modified in a text editor as in previous models. The

model was solved and imported into I-DEAS® for post processing. Table 5.4 reports the

stresses along the constant thickness region of the pipe and shows that the longitudinal

safety factor in the base composite at Test pressure, 22.5 ksi, was 4.39 which is 3.25

times the 1.35 safety factor in the hoop direction. The hoop safety factor is nearly

equivalent to the one recorded at Test pressure in Table 3.3.3 while the longitudinal

safety factor shows a 37% improvement for this model. The ratios of longitudinal to

hoop safety factors show a 39% improvement in the constant thickness region of this

model.

The maximum stresses and safety factors for the entire model are shown in Table

5.5. During Test pressure, the longitudinal safety factor in the base composite was 2.93

which is a 40% improvement over the value found in Table 3.3.5 while the hoop safety

showed little change with a drop of 1.5% in this model. It was concluded that this design

is a great improvement over the design that was produced and tested, but further analysis

was performed to determine the effects of increasing the thickness of the composite by

10%.

Equivalent material properties were calculated in Microsoft® Excel for the 10%

increase. Theses properties as well as thickness values are shown in Table 5.6 and were

used to create a new axisymmetric model in I-DEAS®. The model was solved in

ABAQUS® and the results from the constant thickness region are shown in Table 5.7. It

is seen that the safety factors in the base composite increased over the previous model but

the ratio of the longitudinal safety factor to the hoop safety factor is 3.26, which is nearly

104

the same as the last model. The maximum stresses and factors of safety for the entire

model are displayed in Table 5.8. From the analysis results it was determined that while

the safety factors increased and would promote a higher burst pressure, the composite

thickness was increased and would add more weight to the prototype. So it was decided

that the original TR50/Kevlar® 49 design was a more practical and efficient design, and

therefore is recommended for the second prototype.

105

Table 5.1 – Fiber properties of TR50 and Kevlar® 49.

TR50 Kevlar Ef [psi] = 3.45E+07 1.90E+07 εεεεf [%]

=

1.29E+00 1.80E+00

σσσσf [psi]

=

5.26E+05 5.25E+05

Table 5.2 – Orthotropic elastic material properties of TR50 and Kevlar® 49 in separate unidirectional lay-ups.

TR50 Kevlar® 49 E1 = 2.08E+07 1.15E+07 E2 = 1.67E+06 1.60E+06 E3 = 1.67E+06 1.60E+06 G12 = 4.50E+05 4.37E+05 G13 = 4.50E+05 4.37E+05 G23 = 3.98E+05 3.88E+05 νννν12

= 2.84E-01 3.62E-01 νννν13

= 2.84E-01 3.62E-01 νννν23

= 5.73E-01 5.73E-01 νννν32

= 5.73E-01 5.73E-01 νννν21

= 2.27E-02 5.01E-02 νννν31

= 2.27E-02 5.01E-02

Table 5.3 – Modified design describing composite thickness, liner thickness and equivalent orthotropic elastic material properties for TR50 and Kevlar® 49 in a [±±±±20°°°°,90°°°°] lay-up.

Ex [psi] = 2.13E+06 Ey [psi] = 5.54E+06 Ez [psi] = 1.10E+07

ννννxy

= 0.2049 ννννxz = 0.0806 ννννyz = 0.0967

Gxy [psi] = 4.15E+05 Gxz [psi] = 4.21E+05 Gyz [psi] = 9.92E+05

tkevlar [20] [in] = 0.0906 tTR50[90] [in] = 0.0875 t[20,90] [in] = 0.1781

ts [in] = 0.0650 σσσσs [psi]

= 1.20E+05

106

Table 5.4 – FEA results for the constant thickness section of the TR50/Kevlar® design.

tsteel = .065 t[±20°,90°] = .178 w/ 120ksi Steel Liner σσσσVon Mises [ksi]

σσσσYield [ksi]


S.F. Test 120.40 120.00 1.00 126.78 1.05 Zero 89.51 120.00 1.34 126.78 1.42 Work 64.14 120.00 1.87 126.78 1.98 Burst 120.76 120.00 0.99 127.78 1.06 [20,90] σσσσhoop [ksi]


σσσσlong [ksi]


107

Table 5.5 – Maximum stresses and factors of safety from the finite element analysis of the TR50/Kevlar® design.


σσσσYield [ksi]




σσσσYield [ksi]




σσσσlong [ksi]

FPFlong [ksi] S.F. FFlong [ksi] S.F. Test 42.20 11.56 0.27 123.50 2.93 Zero 17.20 11.56 0.67 123.50 7.18 Work 34.00 11.56 0.34 123.50 3.63 Burst 76.01 11.56 0.15 123.50 1.62 [90] σσσσhoop [ksi]


σσσσlong [ksi]


108

Table 5.6 – Modified design of TR50 and Kevlar® 49 in a [±±±±20°°°°,90°°°°] lay-up with a 10% increase in base composite thickness.

Ex [psi] = 2.13E+06 Ey [psi] = 5.54E+06 Ez [psi] = 1.10E+07

ννννxy

= 0.2049 ννννxz = 0.0806 ννννyz = 0.0967

Gxy [psi] = 4.15E+05 Gxz [psi] = 4.21E+05 Gyz [psi] = 9.92E+05

tkevlar [20] [in] = 0.0992 tTR50[90] [in] = 0.0959 t[20,90] [in] = 0.1951

ts [in] = 0.0650 σσσσs [psi]

= 1.20E+05

Table 5.7 – FEA results for the constant thickness section of the TR50/Kevlar® design with a 10%

increase in base composite thickness.

tsteel = .065 t[±20°,90°] = .195 w/ 120ksi Steel Sleeve σσσσVon Mises [ksi]

σσσσYield [ksi]


S.F. Test 120.30 120.00 1.00 126.78 1.05 Zero 83.95 120.00 1.43 126.78 1.51 Work 65.13 120.00 1.84 126.78 1.95

120.70 120.00 0.99 127.78 1.06 [20,90] σσσσhoop [ksi]


σσσσlong [ksi]


109

Table 5.8 – Maximum stresses and factors of safety from the TR50/Kevlar® design with a 10% increase in base composite thickness.


σσσσYield [ksi]




σσσσYield [ksi]




σσσσlong [ksi]

FPFlong [ksi] S.F. FFlong [ksi] S.F. Test 41.10 11.56 0.28 123.50 3.00 Zero 15.50 11.56 0.75 123.50 7.97 Work 32.60 11.56 0.35 123.50 3.79 Burst 73.90 11.56 0.16 123.50 1.67 [90] σσσσhoop [ksi]


σσσσlong [ksi]


110

Figure 5.1 – Exploded view of the sleeve model with base and reinforcement composites modeled as a single part.

[90º] Reinforcing Composite

[±20º, 90º] Base Composite

Hump/Fitting Sleeve

Liner

111

Chapter Six

Conclusions and Recommendations

6.1 Conclusions

The main objective of this research was to design a lightweight replacement for

an all-steel pipe used by the Halliburton Company for hydraulic fracturing. The

incorporation of high strength composite materials and autofrettage was the cornerstone

of the design. The initial design using a bi-directional laminate was shown to be inferior

to the weight reduction capabilities of a three-directional lay-up. A [±20º, 90º] lay-up

was determined to be more effective when dealing with the bi-directional (hoop and

longitudinal) loading inflicted on a pipe through pressurization. It was also realized that

for this application steel with high yield strength is more efficient than low yield strength

steel.

Initially it was thought that an existing all-steel pipe could be modified and used

as the liner on which the composite would be filament wound. This idea was abandoned

because after the pipe is machined to a thickness less than its original, its ability to bear

longitudinal stress would be diminished in a manner for which the composite is unable to

compensate. So the hump design was formed consisting of two custom end fittings

welded to a thin-walled tube. It was concluded that such a design was efficient but the

location of the weld would be a concentration point for erosion/corrosion, so the sleeve

design was proposed in which the hump/fitting fits over the liner and is welded at its end.

Lastly, a loading scenario was discovered which required a method to transfer

torque from the fitting to the composite thereby avoiding damage to the thin-walled liner.

The track design was implemented and proved to be effective for this purpose.

112

The pipe was fabricated and weighed 74 lbs, a weight difference of 29.5% less

than the all-steel pipe. The prototype was tested successfully to the autofrettage pressure

of 22.5 ksi and then pressurized to failure at 29.4 ksi. The burst pressure was nearly

equal to the predicted value of 30.0 ksi, however, the pipe did not fail as expected.

Results from FEA showed that the pipe would fail in the hoop direction resulting in

longitudinal splitting, but the test showed that the pipe started to split and then broke into

three separate parts. It was concluded that once the hoop-wound fibers failed, the hoop

stress was transferred to the ±20º fibers causing their failure.

The design was modified by replacing the ±20º TR50 fibers with Kevlar® 49

fibers so that the greater elongation to failure of Kevlar® would promote failure of the

hoop-wound fibers at burst pressure. Analysis showed that the modified design resulted

in a greater safety factor in the longitudinal direction while the hoop safety factor

remained nearly the same. It was determined that this design modification was an

improvement and would be recommended for the second prototype for future fabrication

and testing.

6.2 Recommendations

Recommendations to refine and optimize the design of the hybrid steel/composite

pipe for high pressure applications are as follows:

• Optimize the design of the humps and fittings to reduce weight. Consider thickness

reduction of the large humps, the reduction of space between humps or possibly

single hump fittings.

113

• Consider the use of triangular shaped raised guides for the fibers coming out of the

tracks to have better alignment at the turnaround region. Figure 6.2.1 is a possible

design for the riser.

• Align the fittings accurately to aid in computer aided filament winding. The four

original prototypes had randomly aligned fittings. Also use a nut-less connector to

simplify winding.

• Consider a bi-directional angle less than ±20º for the longitudinal fibers in the base

composite. As the angle approaches 0º, the amount of hoop stress loaded on these

fibers also moves toward zero and should promote the desired longitudinal splitting

during failure.

• Optimize the thickness of the 90º reinforcement layer over the humps. Consider

using the reinforcement between the inner and outer hump only and not on top of the

humps or between the track/hump and the fitting. Calculations were not performed to

determine the required thickness of reinforcement, but instead 0.125 inch was chosen.

• Study the effects of changing the selected autofrettage pressure.

• Evaluate padding materials and resin systems for impact and abrasion resistance.

• Consider application of padding layer between CFRP and abrasion/impact resistant

outer layer of GFRP for greater distribution of impact.

114

Figure 6.2.1 – Possible design of raised guides for aiding fiber alignment upon

exiting the tracks into the turnaround area.

Triangular Raised Guide

115

References

1. Spencer, B.E., “Advancing the Use of Composites in the Oil Field,” SAMPE

Journal, Vol. 34, No. 4, July/August 1998, p. 20-25.

2. Lubin, G. et al, Handbook of Composites, Van Nostrand Reinhold Company, 1982.

3. Chung, D.D.L., Carbon Fiber Composites, Butterworth-Heineman, 1994.

4. Jianrong, Y., Fangjing, X. and Yuande, X., “A Study on Failure Behavior of Hybrid Composites Under Static and Fatigue Tortional Loading,” Composites, Proceedings of the Eighth International Conference on Composite Materials (ICCM/8), Honolulu, July 15-19, SAMPE, 1991.

5. Glenn, T. A., Chen, J. and Sherwood, J. A., “Carbon/Glass Hybridization: Another Degree of Design Freedom for Composite Structures,” SAMPE Journal, Vol. 34, No. 3, May/June 1998, p. 22-31.

6. Agarwal, B. D. and Broutman, L. J., Analysis and Performance of Fiber Composites, John Wiley & Sons, 1990.

7. Potter, K. D., Wismon, M. R., Lowson, M. V. and Adams, R. D., “Innovative Approaches to composite structures,” The Aeronautical Journal, February 1998, p. 107-111.

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10. Harvey, W. A. and Kremer, J. S., “Design, Process Development, and Fabrication of an All IM7/977-2 12 In. Dia. Pressurized Fuel Line Required to Operate at -423ºF While Bolted to an Aluminum Valve,” 42nd International SAMPE Symposium, May 4-8, 1997, p. 839-853.

11. Segall, A. E., Tricou, C., Evanko, M. and Conway, Jr., J. C., “Localized Autofrettage as a Design Tool for the Fatigue Improvement of Cross-Bored Cylinders,” Journal of Pressure Vessel Technology, Vol. 120, November 1998, p. 393-397.

12. Underwood, J. H., Parker, A. P., Corrigan, D. J. and Audino, M.J., “Fatigue Life Measurements and Analysis for Overstrained Tubes with Evacuator Holes,” Transactions of the ASME, Vol. 118, November 1996, p. 424-428.

13. Hussain, M. A., Pu, S. L., Vasilakis, J. D. and O’Hara, P., “Simulation of Partial Autofrettage by Thermal Loads,” Journal of pressure Vessel Technology Technical Briefs, August 1980, Vol. 102, p. 314-318.

116

14. Feng, H., Mughrabi, H. and Donth, B., “Finite-Element Modelling of Low-

Temperature Autofrettage of Thick-Walled Tubes ot the Austenitic Stainless Steel AISI 304 L: Part I. Smooth Thick-walled Tubes,” Modelling and Simulation in materials Science and Engineering 6, 1998, p. 51-69.

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117

Appendix A:

Instructions for Modification and

Analysis of the Hybrid Steel/Composite

Pipe Using SDRC® I-DEAS® and

ABAQUS®

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Modifying the Model for a New Composite Design

Open File BASEPIPE.mf1 in IDEAS, and “Save As” a new file.

Go to “Master Modeler”.

Click and hold the highlighted icon and select “Manage Bin”.

Find “ASSEMBLYtemp”, click on it to highlight it, then click (get),

then click on “comp curves temp” and get, then “Dismiss”.

Note: You can change the viewpoint with Pan, Zoom, or Rotate using F1,

F2, or F3 respectively. Hold down one of these buttons while moving the

mouse. You can also use the highlighted icons:

Note: Save often, IDEAS has a very limited “Undo”. The model maybe

closed and reopened without saving, this will open the model without the most

recent changes.

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The green lines and curves are the composite and the red surfaces are

the steel sleeve and humps. The steel will probably stay the same for a new

design so these directions will focus on changing the composite only.

The first step is to move all straight vertical lines (red arrow)

according to the dimensions of the new design. Do not move the lines and

curves, which are closest to the red surfaces (blue arrow). Notice that there

are two layers of composite over the hump section. The layer closest to the

red surface is the 0.21” [+/-20,90] layer and the outer layer is 0.125”

[90] reinforcement.

Click and hold the highlighted icon and select “Move”, then

select all of the vertical lines (hold “Shift” key when selecting more

than one object to move), press “Enter” then type the translation

distance separated by spaces (ex. -.01 0 0).

Next, the angled lines (green arrow) must be moved. Use the

move icon again and after selecting the lines and pressing done

(enter), then select “Move along” from the pop up menu. Pick one of the lines

that are perpendicular to the line you are moving. You will be prompted for

direction along the vector, choose yes if the arrow is pointing in the correct

direction, then enter the translation distance.

Note: Instead of using the move icon for the angled and vertical lines, you

may try using the “Offset” icon. This will create an offset copy of the selected

line, the selected line must be deleted after the offset. Do not use offset to

create the curved sections.

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Now before moving the other angled lines (purple arrow), you need to

trim/extend a few lines.

Click and hold the highlighted icon and select “trim/extend”.

Then select the first line (yellow arrow) close to the second line (green

arrow), then select the second line as the line to “extend to”. Repeat

this process but selecting the second line and then the first line. This

will ensure the contact of the two lines.

Next, move the other angled lines (purple arrow)

using the move icon, and the “Move to” option in the pop-

up menu. When prompted, pick the end of the line (purple

arrow) for the “move from” point and then pick the end of

the line (green arrow) for the “move to” point. This will

create gaps/overlaps elsewhere, which will be fixed later

using the trim/extend icon.

Click and hold the black highlighted icon and

select “Delete” then select the two lines (gray arrow) and press “Enter”.

Using the green highlighted icon, “Trim/Extend” the two remaining lines at

point #2 (both must be trimmed to the other, zoom extremely close to #2 to

see the gap/overlap).

Now click and hold the white highlighted icon and select “Lines”.

Click the right mouse button and select “Focus” (this will allow you to place a

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point on a line by snapping the cursor to the endpoint) then select the

intersection at #1 and then select “Focus” and select intersection #2 and then

repeat this for intersection #3. Now, draw lines from point #1 to #2 and #2 to

#3.

The newly created lines are not associated with the lines and curves of

“comp curves temp”. Click and hold the highlighted icon and select “Attach”.

Select the two new lines while holding the “Shift” button and then press

“Enter”, then select one of the lines (straight or curved) from “comp curves

temp”. The two new lines are now part of “comp curves temp”.

Note: “Trim/Extend” both ends of every single straight line on the part, this

will remove gaps and overlaps (intersections) which would prevent the

creation of surfaces. Make sure both ends of every straight line has

been trim/extended before continuing.

Click and hold the highlighted icon and select “Get”, select

“curve forms” and then “OK”. This part will be used to shape the

spline curves of the humps.

Delete the two outer spline curves over each hump (four curves

total). Do not delete the curves closest to the red surfaces.

Click and hold the highlighted icon and select “Points”. Click

right mouse button and select “Focus”, this will allow you to place a

point on a line by snapping the cursor to the endpoint. Place a point at

each location shown in the figure far right (14 points total).

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Next, click on “Move” and select the points on the upper end of all

the vertical lines (4 points total), click done. Select “Copy sw” from the

pop-up menu and “On”. Type a translation distance of (0 .01 0), press

“Enter” then type 3 for the number of copies, press “Enter”. Repeat this for

the points on the opposite ends of these lines (2 points) but with negative Y

translation. This should result in 4 points at the free ends of each vertical

line (the lines between the humps are shown in the figure to the right).

Then, click “Move” and select the points at the ends of the

two angled lines. Select “Copy sw”, “On”, and “Move Along”.

Select the angled line as the vector to move along, and the direction

would be away from the end of the line. Type the translation

distance of .01 but this time make only one copy. This should

result in two points at the bottom end of both angled lines, as

shown in the figure to the right.

Now the points on the “curve forms” must be moved/copied

to shape the spline curves of the humps. Click “Move” and then

select one of the points on the curve, press “Enter” and then pick

“Move Along” from the pop down menu and click the line

corresponding to that point for the “vector to move along”. Select

the direction pointing away from the hump and enter the distance

according to the thickness of the new design. Then move and copy

the same point along the same line with a translation distance of

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.125”, the thickness of the outer layer of the composite. These steps should be

repeated for the other 5 points over the humps. This should result in 6 points

over each hump. These will be used to form the two outer curves over each

hump.

Now that the base points have been placed, the splines can

be created. Zoom the view to the top half of the top hump. Click

and hold the highlighted icon and select “Splines”. Select the

points according to the numbering in the picture to the right. If the

pointer doesn’t automatically snap to the points then zoom by hand

using F2. Then before pressing “Enter”, hold F1 to pan the view

downward to the next 4 points, and continue selecting the points as

numbered and press “Enter” after selecting point #9. Repeat with the inner

points but in the opposite order, starting at the bottom points and move to the

top points. It is important that these lines are drawn in a clockwise direction

with respect to the part.

Repeat the creation of the splines on the bottom hump in the same

manner as above. From top to bottom on the outside line and from bottom to

top on the inside line.

Put away “curve forms” and “ASSEMBLYtemp”.

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The newly created splines are not associated with the lines and curves

of “comp curves temp”. Click and hold the highlighted icon and select

“Attach”. Select the four spline curves while holding the “Shift” button and

then press “Enter”, then select one of the lines (straight or curved) from

“comp curves temp”.

Note: To be sure the new splines are attached, click “Put Away” and select

one of the vertical lines and if all the lines and curves disappear, including the

new splines, then the “Attach” process was performed correctly. Now use

“Manage Bin” or “Get” to get “comp curves temp” out of the manage bin.

Click the highlighted icon, “Delete”. Click the right mouse button and

select “Filter” from the pop-up menu, then from the “Filter” window, select

“Point…” and click on “Pick Only”, then click the right mouse button and

select “All” from the pop-up menu, press “Enter” and then “Yes”.

Select “Manage Bin” and highlight “comp curves temp”, click “Put

Away” and then click on (“Copy”), fill out the fields in the pop-up

window, name it “Comp Curves” in the “Main” bin (part number not

necessary). Now, select “Comp Curves” and click “Get” then “Dismiss”.

By pressing Ctrl + M on the keyboard an additional menu (on left side

of graphics window) may be displayed or hidden. Display this menu if not

visible.

There may be more than one menu displayed, select “Create” from the

main menu (far left), then select “Planar Surface” from the submenu. Select

the outer lines and curves one at a time with the mouse. Zooming with F2

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may be necessary to avoid picking the interior lines. After all outer lines

have been selected, they will change to a thicker line with a different color

as seen in the picture to the right (the color may vary), press “Enter”.

These lines will now be regular thickness but a different color than the

former green lines and curves. This is now a surface. Notice that many of

the interior lines have disappeared as shown in the figure far right. The

lines and curves that disappeared are needed to partition the part.

Click on the “Delete” icon, then click the right mouse button and

pick “Filter” from the pop-up menu. Select “Curve…” and click “Pick

Only”, then click the right mouse button and select “All” and press “Enter”

and then “Yes”.

Go to “Manage Bin” and highlight “comp curves temp”, click on the

“Copy” icon and then click “OK” when the “Copy” window pops up.

Highlight “Part1” and click “Get”, then “Dismiss”.

Zoom in so the display matches the figure to the right. Click

and hold the highlighted icon and then select “Extrude”. Select

ALL the interior perpendicular lines (blue arrow) one at a time

while hitting “Enter” only once after each one or two part line is

selected (ex. of a two part line, white arrow). The lines will change

color and thickness. Note: If unable to select some of the two part

lines in a consecutive manner, then the lines have not been properly

trimmed or extended, click the right mouse button and select “Cancel” from

the pop-up menu then trim/extend the lines and then attempt to extrude.

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Note: If the wrong line is selected by accident then click the right mouse

button and select “Backup” from the pop-up menu. After the lines in the

current view have been selected, use F1 to pan the screen down to the next

perpendicular lines and select them for extrusion. Do not select the perimeter

line at the very bottom of the part, select only the interior lines. After

selection is complete, press “Enter” and “Extrude Section” window will pop

up. Change the “Distance” to .1 and change to “Thicken”

and click “OK”. Notice that some of the lines disappeared after this

operation.

Click on the “Delete” icon, then click the right mouse button and pick

“Filter” from the pop-up menu. Select “Curve…” and click “Pick Only”, then

click the right mouse button and select “All” and press “Enter”.

Click and hold the highlighted icon and select “Partition”. Select one

of the perpendicular lines that were extruded as the “partitioning part” and

then select one of the perimeter lines as the “part to partition”. This will

divide the composite surface into several surfaces.

Go to “Manage Bin” and highlight “Part1” and click “Delete”.

Highlight “comp curves temp” and click “Copy” and then click “OK”. Select

“Part1” then “Get” then “Dismiss”.

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Select “Extrude” and select the internal lines and curves (white

highlighted) parallel to the perimeter. Select these without pressing “Enter”

after each one. After all have been selected, press “Enter” Change the

“Distance” to .1 and change to “Thicken” and click “OK”.

Note: If unable to select some of the lines in a consecutive manner, then the

lines have not been properly trimmed or extended, click the right mouse

button and select “Cancel” from the pop-up menu then trim/extend the lines

and then attempt to extrude.

Click on the “Delete” icon, then click the right mouse button and pick

“Filter” from the pop-up menu. Select “Curve…” and click “Pick Only”, then

click the right mouse button and select “All” and press “Enter”.

Select “Partition” and select the newly extruded curve as the

“partitioning part” and then select one of the perimeter lines as the “part to

partition”.

Zoom to the region in the figure to the far right. Click and

hold the black highlighted icon and select “Sketch in place” and

then any line on the composite. The surface will change to thick

blue lines.

Select “Lines” from the white highlighted icon. Draw lines

from #1 to #2 and #2 to #3. The selector arrow should snap to the

intersection #1 and the two midpoints #2 and #3.

Select “Extrude” from the green highlighted icon above. Click the

right mouse button and select “Partition” from the pop up menu and then

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select the new green lines and press “Enter” twice and then “OK” in the

“Extrude” window.

Go to “Manage Bin” and highlight “Part1” and click “Delete”. Select

“ASSEMBLYtemp” and “Get” and “Dismiss”.

Go to “Meshing”.

Click and hold the highlighted icon and select “Create FE Model”.

Click then select the composite then “OK”. Repeat this and select the

steel.

Use “Ctrl + M” to display the additional menus if not visible. Select

“Manage” from the menu and “Append” from its submenu. The “Select

source FE Model” window will appear. If “Comp Curves” is displayed as

“Comp Curves…” then double click it to reveal its contents. Select “Fem1”

below “Comp Curves” and click “OK”. The “Select destination FE Model”

window will appear. Select “Fem1” below “ASSEMBLYtemp” and click

“OK”.

Go to “Master Modeler”.

Go to “Manage Bin” and select “Comp Curves”, “Put Away” and “Dismiss”.

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Click and hold the black highlighted icon, select “Sketch

in place” and then select the steel hump section anywhere between

the sleeve and the composite. The humps section will change to

thick blue lines as shown in the picture to the far right.

Zoom to the region pictured to the far right. Select

“Lines” from the white highlighted icon. Draw freehand lines

from the three intersection points on the blue surface in a normal

direction (as accurate as possible) to the curves as shown in the picture above

far right. Continue on with the last four and then select “Trim/Extend” from

the green highlighted icon and trim all of the lines to fit within the composite

as shown with line #5.

Select the “Extrude” icon then click the right mouse button and select

“Partition” from the pop up menu. Select all of the new lines and press

“Enter”. Click “OK” in the “Extrude section” window.

Select “Sketch in place” and then select the steel hump section

anywhere between the sleeve and the composite. Repeat the processes of

creating lines, trimming and partitioning on the bottom hump. The model

should look like the figure to the right (color may differ).

“Save” the changes to the model file and then “Save as” and change

the file name. This is done for protection in the event that the working file

becomes corrupt.

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Meshing the New Pipe Design Go to “Meshing”.

Click and hold the highlighted icon and select “Define

Shell Mesh…”. Select the region shown in the figure to the far

right by clicking and dragging a box around those surfaces shown,

then press “Enter”. The “Define Mesh” window will appear, select

and change “Element Family” to

then change “Element Type” to and click on

. The “Mapped Meshing Options” window

appears. Select and when prompted to “Pick any 3 or 4

among highlighted vertices (all)”, press enter repeatedly until all surfaces

are defined and the “Mapped Meshing Options” window reappears. Select

, and when prompted to “Enter number ( > 0 ) of

elements for highlighted sides (1)”, type “6” for each vertical edge and “1”

for the horizontal edge of the sleeve and “2” for the rest of the horizontal

edges as shown in the figure to the right. When the “Mapped Meshing

Options” window reappears, select “Dismiss”. Select “Set As Default”, then

select to preview the mesh, and press “Keep Mesh”.

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Pan the view up to the region shown in the figure to the right.

Define a mesh, for the two selected surfaces in the figure, following the above

procedure and defining the number of elements along the vertical edges to be

“13”.

Pan the view up to the region shown in the figure to the right. Define

a mesh, for the selected surfaces in the figure, following the above procedure

define the number of elements along the vertical edges as shown in the figure.

Define a mesh, for the 3 selected surfaces in the figure, set the number

of elements along the vertical edges to be the same as the elements on the

sleeve defined above. Define the number of elements along the horizontal

edges as shown in the figure.

Define a mesh, for the 2 unmeshed surfaces between the 3 selected

surfaces in the figure. Choose , change “Element Family” to

and “Element Type” to . Select to

preview the mesh and then select “Keep Mesh”. These two surfaces should

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look about like the figure to the right, with triangular elements to step up from

2 to 3 rectangular elements and from 3 to 4 rectangular elements.


a mesh for the selected surfaces. Set the number of elements along the

vertical edges as shown in the figure.




edges as shown in the figure to the right.

Define a mesh, for the 3 unmeshed surfaces between and below the 3

selected surfaces in the figure. Choose , change “Element Family” to

and “Element Type” to . Select to

preview the mesh and then select “Keep Mesh”. These three surfaces should

have triangular elements to step down from 4 to 3 rectangular elements, from

3 to 2 rectangular elements and from 2 to 1 rectangular elements.

133







edges as shown in the figure to the right.

Define a mesh, for the 3 unmeshed surfaces between the selected

surfaces in the figure. Choose , change “Element Family” to

and “Element Type” to . Select to preview

the mesh and then select “Keep Mesh”. These three surfaces should have

triangular elements to step up from 1 to 2 rectangular elements, from 2 to 3

rectangular elements and down from 3 to 2 rectangular elements.




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Define a mesh, for the selected surface in the figure, set the number of

elements along the vertical edges to be the same as the elements on the sleeve

defined above. Define the number of elements along the horizontal edges as

shown in the figure to the right.

Define a mesh, for the unmeshed surfaces below the selected surface

in the figure on the previous page. Choose , change “Element Family”

to and “Element Type” to . Select to

preview the mesh and then select “Keep Mesh”. This surface should look

about like the figure to the right, with triangular elements to step down from 2

to 1 rectangular elements.

Pan the view up to the region shown in the figure to the right. The

sleeve only has two unmeshed surfaces at this point. Define a mesh for these

two surfaces. Set the number of elements along the vertical edges to be 6 for

the short lower surface and 110 for the long upper surface.

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The steel sleeve and humps should now be completely meshed and

should resemble the figure pictured to the right. The next step is to mesh the

inner layer of composite.

Change the view to the region shown in the figure to the right. Define

a mapped mesh for the 5 selected surfaces. In the “Define Mesh” window,

change the “Material:” to “Other” and click the “Material Selection…” icon.

Choose “Material Type Filter…” and select “ORTHOTROPIC

MATERIALS” in “Finite Element Modeling”, click “OK”. Highlight

“COMP2090”, click “OK”. Click on the “Set As Default” icon. In “Mapped

Options…” set the number of elements along the vertical edges to be the same

as the number of elements on the steel beside it. Define the number of

elements along the horizontal edges to be 2.

136

Pan the view to the region shown in the figure to the right. Define a

mapped mesh for the 11 selected surfaces. Follow the procedure above. The

mesh should match the figure to the far right.


mapped mesh for the 7 selected surfaces. Follow the procedure above. The

mesh should match the figure to the far right.


free mesh for the 2 surfaces (red arrow). Follow the procedure above to create

one element on each surface. Then define a mesh for the triangular surface

(blue arrow). Use , and then click

the preview icon and “Keep Mesh”.

137


mapped mesh for the remaining 3 surfaces on the inner composite layer.

Follow the procedure for map meshing. The mesh should match the figure to

the far right. Set the number of elements along the vertical edges to be 1 for

the short lower surface, 6 for the middle surface and 110 for the long upper

surface.

The inner composite layer should now be completely meshed and

should resemble the figure pictured to the right. The next step is to mesh the

outer layer of composite.

138


mapped mesh for the 10 selected surfaces. In the “Define Mesh” window,

change the “Material:” to “Other” and click the “Material Selection…” icon.

Choose “Material Type Filter…” and select “ORTHOTROPIC

MATERIALS” in “Finite Element Modeling”, click “OK”. Highlight

“COMP90”, click “OK”. Click on the “Set As Default” icon. Follow the

procedure for map meshing and define 1 element through the horizontal

thickness.


mapped mesh for the remaining 16 surfaces. Follow the procedure for map

meshing.

The outer composite layer should now be completely meshed and

should resemble the figure pictured to the far right.

139

Select the black highlighted icon, select the green highlighted icon

form the pop up window. Hold the right mouse button, select “Filter”, select

“Node” then “Pick Only”. Hold the right mouse button again, select

“Related To”, hold the right mouse button, select “Filter”, “Edge” then

“Pick Only”. Hold the right mouse button and select “All” then press

“Enter” twice and then type “gap nodes” when asked to “Enter PERMANENT

GROUP name or no.”

Select the white highlighted icon in the pop up window then hold the

right mouse button, select “Filter”, “Edge” and “Pick Only”. Hold the right

mouse button and select “All Done”. Select the red highlighted icon in the

pop up window, this will display the newly created group. Press Ctrl+M to

bring up the additional menus, select “Display Options” > “Node” >

“Asterisk”. Then select the blue highlighted icon to redraw the display.

Zoom in on the region shown to the far right. Click and hold

the highlighted icon and select “Element”. In the “Element” window

select , then , then and “OK”.

Click and drag a box around the nodes as show in the figure to the far

right. Repeat this process for ALL nodes along the gaps. This should

result in gap elements between every pair of nodes between the sleeve

and composite, sleeve and humps, and humps and composite, as

shown in the figure lower far right.

140

Zoom out and the model should look like the figure to the right. Now

press “Ctrl+M” to display the additional menus and select “Display Options”

> “Node” > “Dot”, then redraw using the “Redraw” icon.

The meshing should now be complete. The next step is to define the

boundary conditions. Save the model file.

141

Defining Boundary Conditions for the New Pipe Design Go to “Boundary Conditions”.

Zoom to the region shown in the figure to the far right.

Select “Displacement Restraint…” from the highlighted icon and

drag a box around the selected edge (white box) exactly as shown in

the figure, then press “Enter” and “Node”. The “Displacement

Restraint on Node” window will appear. Select and

. Then select and change “Y Translation”

to , select “OK” and then “OK”.

Zoom to the region shown in the figure to the far right.

Select “Coupled DOF…” from the highlighted icon and click on the

independent node (red arrow) and then drag a box around the

dependent nodes (white box) exactly as shown in the figure to the

far right, press “Enter”. The “Coupled Degrees of Freedom”

window will appear. Change the “Y Translation” to ,

select “OK”.

142

Select “Force…” from the highlighted icon and click the

right mouse button and select “Filter” > “Node” > “Pick Only”

and then select the node (blue arrow) shown in the figure to the

far right and press “Enter”. The “Force on Node” window will

appear. Change “Y Force” to “-3.14159” and select “OK”.

Zoom to the region shown in the figure to the right. Select “Force…”

from the icon menu and click the right mouse button and select “Filter” >

“Element_Free_Edge” > “Pick Only”. Drag a box around the inner edge of

the elements on the sleeve as shown to the right (all elements along the inner

edge of the sleeve will be selected eventually so accuracy on the number of

elements in this selection is not important). Now before pressing “Enter”,

click the right mouse button and select “Highlight Selection” and then pan the

view upwards using the “F1” key and drag a box, while holding the “Shift”

key, around the unselected “Element_Free_Edges”. Repeat the above steps

until all “Element_Free_Edges” along the inner edge of the sleeve has been

selected and then press “Enter”. The “Force on Element Edge” window will

appear. Change the “In Plane Force” to start with an amplitude of “1” and end

with an amplitude of “1” then select “OK”. The model should have a

distributed load along the length of the sleeve as shown in the figure to the

right.

143

Select the highlighted icon and then select and

then click on “LOAD SET 1” to highlight it, then press

“OK”.

Save the file.

From the “File” menu, select “Export” > “ABAQUS” > “OK”. The

“ABAQUS File Exporter” window will appear. The filename and path may

be changed, the default will be saved to the C: drive or the drive from which

IDEAS is running. Select then

and select “Stress”, “Strain”, “Plastic Strain” and “Displacement” for output

and select “OK”. Select from the “ABAQUS History

Definition” window and change “Maximum Number of Increments” to

“10000” and change “Amplitude Loading Type” to “Ramp”, select “OK”.

Select “Apply” from the “ABAQUS History Definition” window then select

“OK”. Select “Write” from the “ABAQUS File Exporter” window.

144

Editing the ABAQUS Input File

Open the ABAQUS input file in “WordPad” (or “Notepad”) for text

editing. Go to the bottom and then slowly scroll up until “*SOLID SECTION,” is

seen. Delete the highlighted lines below:

*SOLID SECTION,ELSET=AXISYMMETRIC SOLID2 ,MATERIAL=GENERIC_ISOTROPIC_STEEL*MATERIAL,NAME=GENERIC_ISOTROPIC_STEEL*ELASTIC,TYPE=ISOTROPIC2.99938E+07, 2.90000E-01*DENSITY7.31737E-04,*EXPANSION,TYPE=ISO,ZERO=71.336.50000E-06,*CONDUCTIVITY,TYPE=ISO5.62022E+00,*SOLID SECTION,ELSET=AXISYMMETRIC SOLID2_1 ,MATERIAL=COMP2090*MATERIAL,NAME=COMP2090*ELASTIC,TYPE=ENGINEERING CONSTANTS2.999E+07, 2.999E+07, 2.999E+07, 2.900E-01, 2.900E-01, 2.900E-01, 1.162E+07, 1.162E+071.162E+07,*DENSITY7.31737E-04,*EXPANSION,TYPE=ORTHO,ZERO=71.336.50000E-06, 6.50000E-06, 6.50000E-06*CONDUCTIVITY,TYPE=ORTHO5.62022E+00, 5.62022E+00, 5.62022E+00*SOLID SECTION,ELSET=AXISYMMETRIC SOLID2_2 ,MATERIAL=GENERIC_ISOTROPIC_STEEL*SOLID SECTION,ELSET=AXISYMMETRIC SOLID2_3 ,MATERIAL=COMP2090*SOLID SECTION,ELSET=AXISYMMETRIC SOLID2_4 ,MATERIAL=COMP90*MATERIAL,NAME=COMP90*ELASTIC,TYPE=ENGINEERING CONSTANTS2.999E+07, 2.999E+07, 2.999E+07, 2.900E-01, 2.900E-01, 2.900E-01, 1.162E+07, 1.162E+071.162E+07,*DENSITY7.31737E-04,*EXPANSION,TYPE=ORTHO,ZERO=71.336.50000E-06, 6.50000E-06, 6.50000E-06*CONDUCTIVITY,TYPE=ORTHO5.62022E+00, 5.62022E+00, 5.62022E+00

145

This section should now look similar to the text below: *SOLID SECTION,ELSET=AXISYMMETRIC SOLID2 ,MATERIAL=GENERIC_ISOTROPIC_STEEL*MATERIAL,NAME=GENERIC_ISOTROPIC_STEEL*ELASTIC,TYPE=ISOTROPIC2.99938E+07, 2.90000E-01*SOLID SECTION,ELSET=AXISYMMETRIC SOLID2_1 ,MATERIAL=COMP2090*MATERIAL,NAME=COMP2090*ELASTIC,TYPE=ENGINEERING CONSTANTS2.999E+07, 2.999E+07, 2.999E+07, 2.900E-01, 2.900E-01, 2.900E-01, 1.162E+07, 1.162E+071.162E+07,*SOLID SECTION,ELSET=AXISYMMETRIC SOLID2_2 ,MATERIAL=GENERIC_ISOTROPIC_STEEL*SOLID SECTION,ELSET=AXISYMMETRIC SOLID2_3 ,MATERIAL=COMP2090*SOLID SECTION,ELSET=AXISYMMETRIC SOLID2_4 ,MATERIAL=COMP90*MATERIAL,NAME=COMP90*ELASTIC,TYPE=ENGINEERING CONSTANTS2.999E+07, 2.999E+07, 2.999E+07, 2.900E-01, 2.900E-01, 2.900E-01, 1.162E+07, 1.162E+071.162E+07,

Now define the plastic material definition of the steel by adding the following three

highlighted lines as shown:

*SOLID SECTION,ELSET=AXISYMMETRIC SOLID2 ,MATERIAL=GENERIC_ISOTROPIC_STEEL*MATERIAL,NAME=GENERIC_ISOTROPIC_STEEL*ELASTIC,TYPE=ISOTROPIC2.99938E+07, 2.90000E-01*PLASTIC, HARDENING=ISOTROPIC120000,0.0126000,0.18*SOLID SECTION,ELSET=AXISYMMETRIC SOLID2_1 ,MATERIAL=COMP2090*MATERIAL,NAME=COMP2090*ELASTIC,TYPE=ENGINEERING CONSTANTS

146

Now modify the properties of [20,90] composite and [90] composite to match

those calculated in Excel by changing the four yellow highlighted lines below:

*SOLID SECTION,ELSET=AXISYMMETRIC SOLID2_1 ,MATERIAL=COMP2090*MATERIAL,NAME=COMP2090*ELASTIC,TYPE=ENGINEERING CONSTANTS2.999E+07, 2.999E+07, 2.999E+07, 2.900E-01, 2.900E-01, 2.900E-01, 1.162E+07, 1.162E+071.162E+07,*SOLID SECTION,ELSET=AXISYMMETRIC SOLID2_2 ,MATERIAL=GENERIC_ISOTROPIC_STEEL*SOLID SECTION,ELSET=AXISYMMETRIC SOLID2_3 ,MATERIAL=COMP2090*SOLID SECTION,ELSET=AXISYMMETRIC SOLID2_4 ,MATERIAL=COMP90*MATERIAL,NAME=COMP90*ELASTIC,TYPE=ENGINEERING CONSTANTS2.999E+07, 2.999E+07, 2.999E+07, 2.900E-01, 2.900E-01, 2.900E-01, 1.162E+07, 1.162E+071.162E+07,

Now go scroll down until “*STEP,AMPLITUDE=RAMP,INC=10000” is seen. Add the

highlighted lines as shown below:

*******************************LOADS**********************************AMPLITUDE,NAME=TEST.1 , 15000. , .2 , 17500. , .3 , 20000. , 1. , 22500.*AMPLITUDE,NAME=ZERO.1 , 22500. , 1.0 , 0.*AMPLITUDE,NAME=WORK.1 , 0.0 , 1. , 15000.*******************************TEST***********************************STEP,AMPLITUDE=RAMP,INC=10000TEST*STATIC**% BOUNDARY CONDITION SET 1**% RESTRAINT SET 1*BOUNDARY,OP=NEWBS000001, 2,, 0.00000E+00**% LOAD SET 1*DLOAD,OP=NEWBS000002, P2, 1.0000E+00

325, P3, 1.0000E+00BS000003, P4, 1.0000E+00*CLOAD,OP=NEW

53, 2,-3.1416E+00*NSET,NSET=BS000001

147

Now go to the very bottom and cut the highlighted lines (cut not delete)

2085,2086,2087,3566,3567,3568,3569,3570*ELSET,ELSET=BS00000279,80,81,82,83,84,85,86,87,88,89,90,144,258,259,260263,319,320,321,322,323,324*ELSET,ELSET=BS00000373,74,75,76,77,78,117,118,119,120,121,122,123,124,125,126127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142143,205,206,207,208,209,210,211,212,213,214,241,242,243,244,245246,247,248,249,250,251,252,253,254,255,256,257,261,262,334,335336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447448,449*NODE FILE,FREQUENCY= 1,GLOBAL=YESU,*EL FILE,FREQUENCY= 1,POSITION=NODES,DIRECTIONS=YESS,E,PE*END STEP

Now paste the “cut lines” and add the green highlighted line as shown below:

*******************************TEST***********************************STEP,AMPLITUDE=RAMP,INC=10000TEST*STATIC**% BOUNDARY CONDITION SET 1**% RESTRAINT SET 1*BOUNDARY,OP=NEWBS000001, 2,, 0.00000E+00**% LOAD SET 1*DLOAD,OP=NEWBS000002, P1, 1.0000E+00BS000003, P3, 1.0000E+00*CLOAD,OP=NEW

22, 2,-3.1416E+00*NODE FILE,FREQUENCY= 1,GLOBAL=YESU,*EL FILE,FREQUENCY= 1,POSITION=NODES,DIRECTIONS=YESS,E,PE*END STEP**********************************************************************NSET,NSET=BS00000198,100,387,389,675*ELSET,ELSET=BS00000267,68,69,70,71,72*ELSET,ELSET=BS00000355,56,57,58,59,60,61,62,63,64,65,66,73,74,75,7677,78,79,80,81,82,83,84,85,86,87,88,89,90,91,9293,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204205,206,207,208,209,210,211,212,213,214,215

148

Change the lines “*DLOAD,OP=NEW” and “*CLOAD,OP=NEW” as shown below:

*******************************TEST***********************************STEP,AMPLITUDE=RAMP,INC=10000TEST*STATIC**% BOUNDARY CONDITION SET 1**% RESTRAINT SET 1*BOUNDARY,OP=NEWBS000001, 2,, 0.00000E+00**% LOAD SET 1*DLOAD,AMPLITUDE=TESTBS000002, P1, 1.0000E+00BS000003, P3, 1.0000E+00*CLOAD,AMPLITUDE=TEST

22, 2,-3.1416E+00*NODE FILE,FREQUENCY= 1,GLOBAL=YESU,*EL FILE,FREQUENCY= 1,POSITION=NODES,DIRECTIONS=YESS,E,PE*END STEP*********************************************************************

At this point, copy the highlighted lines below:

*AMPLITUDE,NAME=TEST.1 , 15000. , .2 , 17500. , .3 , 20000. , 1. , 22500.*AMPLITUDE,NAME=ZERO.1 , 22500. , 1.0 , 0.*AMPLITUDE,NAME=WORK.1 , 0.0 , 1. , 15000.*******************************TEST***********************************STEP,AMPLITUDE=RAMP,INC=10000TEST*STATIC**% BOUNDARY CONDITION SET 1**% RESTRAINT SET 1*BOUNDARY,OP=NEWBS000001, 2,, 0.00000E+00**% LOAD SET 1*DLOAD,AMPLITUDE=TESTBS000002, P1, 1.0000E+00BS000003, P3, 1.0000E+00*CLOAD,AMPLITUDE=TEST

22, 2,-3.1416E+00*NODE FILE,FREQUENCY= 1,GLOBAL=YESU,*EL FILE,FREQUENCY= 1,POSITION=NODES,DIRECTIONS=YESS,E,PE*END STEP**********************************************************************NSET,NSET=BS00000198,100,387,389,675*ELSET,ELSET=BS00000267,68,69,70,71,72

149

Paste the “copied lines” twice after the line “*END STEP” to look like this:

*AMPLITUDE,NAME=WORK.1 , 0.0 , 1. , 15000.*******************************TEST***********************************STEP,AMPLITUDE=RAMP,INC=10000TEST*STATIC**% BOUNDARY CONDITION SET 1**% RESTRAINT SET 1*BOUNDARY,OP=NEWBS000001, 2,, 0.00000E+00**% LOAD SET 1*DLOAD,AMPLITUDE=TESTBS000002, P1, 1.0000E+00BS000003, P3, 1.0000E+00*CLOAD,AMPLITUDE=TEST

22, 2,-3.1416E+00*NODE FILE,FREQUENCY= 1,GLOBAL=YESU,*EL FILE,FREQUENCY= 1,POSITION=NODES,DIRECTIONS=YESS,E,PE*END STEP*******************************TEST***********************************STEP,AMPLITUDE=RAMP,INC=10000TEST*STATIC**% BOUNDARY CONDITION SET 1**% RESTRAINT SET 1*BOUNDARY,OP=NEWBS000001, 2,, 0.00000E+00**% LOAD SET 1*DLOAD,AMPLITUDE=TESTBS000002, P1, 1.0000E+00BS000003, P3, 1.0000E+00*CLOAD,AMPLITUDE=TEST

22, 2,-3.1416E+00*NODE FILE,FREQUENCY= 1,GLOBAL=YESU,*EL FILE,FREQUENCY= 1,POSITION=NODES,DIRECTIONS=YESS,E,PE*END STEP*******************************TEST***********************************STEP,AMPLITUDE=RAMP,INC=10000TEST*STATIC**% BOUNDARY CONDITION SET 1**% RESTRAINT SET 1*BOUNDARY,OP=NEWBS000001, 2,, 0.00000E+00**% LOAD SET 1*DLOAD,AMPLITUDE=TESTBS000002, P1, 1.0000E+00BS000003, P3, 1.0000E+00*CLOAD,AMPLITUDE=TEST

22, 2,-3.1416E+00*NODE FILE,FREQUENCY= 1,GLOBAL=YESU,*EL FILE,FREQUENCY= 1,POSITION=NODES,DIRECTIONS=YESS,E,PE*END STEP**********************************************************************NSET,NSET=BS00000198,100,387,389,675*ELSET,ELSET=BS000002

150

Change the highlighted text below:

.1 , 0.0 , 1. , 15000.*******************************TEST***********************************STEP,AMPLITUDE=RAMP,INC=10000TEST*STATIC**% BOUNDARY CONDITION SET 1**% RESTRAINT SET 1*BOUNDARY,OP=NEWBS000001, 2,, 0.00000E+00**% LOAD SET 1*DLOAD,AMPLITUDE=TESTBS000002, P1, 1.0000E+00BS000003, P3, 1.0000E+00*CLOAD,AMPLITUDE=TEST

22, 2,-3.1416E+00*NODE FILE,FREQUENCY= 1,GLOBAL=YESU,*EL FILE,FREQUENCY= 1,POSITION=NODES,DIRECTIONS=YESS,E,PE*END STEP*******************************ZERO***********************************STEP,AMPLITUDE=RAMP,INC=10000ZERO*STATIC**% BOUNDARY CONDITION SET 1**% RESTRAINT SET 1*BOUNDARY,OP=NEWBS000001, 2,, 0.00000E+00**% LOAD SET 1*DLOAD,AMPLITUDE=ZEROBS000002, P1, 1.0000E+00BS000003, P3, 1.0000E+00*CLOAD,AMPLITUDE=ZERO

22, 2,-3.1416E+00*NODE FILE,FREQUENCY= 1,GLOBAL=YESU,*EL FILE,FREQUENCY= 1,POSITION=NODES,DIRECTIONS=YESS,E,PE*END STEP*******************************WORK***********************************STEP,AMPLITUDE=RAMP,INC=10000WORK*STATIC**% BOUNDARY CONDITION SET 1**% RESTRAINT SET 1*BOUNDARY,OP=NEWBS000001, 2,, 0.00000E+00**% LOAD SET 1*DLOAD,AMPLITUDE=WORKBS000002, P1, 1.0000E+00BS000003, P3, 1.0000E+00*CLOAD,AMPLITUDE=WORK

22, 2,-3.1416E+00*NODE FILE,FREQUENCY= 1,GLOBAL=YESU,*EL FILE,FREQUENCY= 1,POSITION=NODES,DIRECTIONS=YESS,E,PE*END STEP**********************************************************************NSET,NSET=BS00000198,100,387,389,675*ELSET,ELSET=BS000002

The model is now ready to be solved. After a solution is met, the model must

be imported back into IDEAS for post-processing.

151

Appendix B:

ABAQUS® Input File (hybrid1.inp)

152

**% ============================================================**%**% I-DEAS 8 ABAQUS STANDARD TRANSLATOR**% FOR ABAQUS VERSION 5.8**%**% MODEL FILE: C:\Pipe\oldpipe\hybrid_with_no_humps.mf1**% INPUT FILE: C:\Pipe\oldpipe\hybrid_with_no_humps.inp**% EXPORTED: AT 15:39:57 ON 12-Apr-01**% PART: steel**% FEM: Fem1**%**% UNITS: IN-Inch (pound f)**% ... LENGTH : inch**% ... TIME : sec**% ... MASS : lbf-sec**2/in**% ... FORCE : pound (lbf)**% ... TEMPERATURE : deg Fahrenheit**%**% SUBSET EXPORT: OFF**%**% NODE ZERO TOLERANCE: OFF**%**% ============================================================**%**%*HEADINGSDRC I-DEAS ABAQUS FILE TRANSLATOR 12-Apr-01 15:39:57*NODE, NSET=ALLNODES, SYSTEM=R

1, 1.8450000E+00, 0.0000000E+00, 0.0000000E+002, 1.7112500E+00, 0.0000000E+00, 0.0000000E+003, 1.8450000E+00, 8.7340000E-01, 0.0000000E+004, 1.7112500E+00, 8.7340000E-01, 0.0000000E+005, 1.5775000E+00, 8.7340000E-01, 0.0000000E+006, 1.5775000E+00,-1.3659240E-16, 0.0000000E+007, 1.5775000E+00, 1.7467000E+00, 0.0000000E+008, 1.4437500E+00, 1.7467000E+00, 0.0000000E+009, 1.4437500E+00, 8.7340000E-01, 0.0000000E+0010, 1.4437500E+00,-2.7318480E-16, 0.0000000E+0011, 1.3100000E+00, 1.7467000E+00, 0.0000000E+0012, 1.3100000E+00, 8.7340000E-01, 0.0000000E+0013, 1.3100000E+00, 0.0000000E+00, 0.0000000E+0014, 1.3100000E+00, 2.6200000E+00, 0.0000000E+0015, 1.1550000E+00, 2.6200000E+00, 0.0000000E+0016, 1.1550000E+00, 1.7467000E+00, 0.0000000E+0017, 1.1550000E+00, 8.7340000E-01, 0.0000000E+0018, 1.1550000E+00, 0.0000000E+00, 0.0000000E+0019, 1.0000000E+00, 2.6200000E+00, 0.0000000E+0020, 1.0000000E+00, 1.7467000E+00, 0.0000000E+0021, 1.0000000E+00, 8.7340000E-01, 0.0000000E+0022, 1.0000000E+00, 0.0000000E+00, 0.0000000E+0023, 1.8450000E+00, 7.2783333E-01, 0.0000000E+0024, 1.8450000E+00, 5.8226667E-01, 0.0000000E+0025, 1.8450000E+00, 4.3670000E-01, 0.0000000E+0026, 1.8450000E+00, 2.9113333E-01, 0.0000000E+0027, 1.8450000E+00, 1.4556667E-01, 0.0000000E+0028, 1.7112500E+00, 1.4556667E-01, 0.0000000E+0029, 1.7112500E+00, 2.9113333E-01, 0.0000000E+0030, 1.7112500E+00, 4.3670000E-01, 0.0000000E+0031, 1.7112500E+00, 5.8226667E-01, 0.0000000E+0032, 1.7112500E+00, 7.2783333E-01, 0.0000000E+0033, 1.5775000E+00, 1.4556667E-01, 0.0000000E+0034, 1.5775000E+00, 2.9113333E-01, 0.0000000E+0035, 1.5775000E+00, 4.3670000E-01, 0.0000000E+0036, 1.5775000E+00, 5.8226667E-01, 0.0000000E+0037, 1.5775000E+00, 7.2783333E-01, 0.0000000E+0038, 1.5775000E+00, 1.6011500E+00, 0.0000000E+0039, 1.5775000E+00, 1.4556000E+00, 0.0000000E+0040, 1.5775000E+00, 1.3100500E+00, 0.0000000E+0041, 1.5775000E+00, 1.1645000E+00, 0.0000000E+0042, 1.5775000E+00, 1.0189500E+00, 0.0000000E+0043, 1.4437500E+00, 1.0189500E+00, 0.0000000E+00

153

44, 1.4437500E+00, 1.1645000E+00, 0.0000000E+0045, 1.4437500E+00, 1.3100500E+00, 0.0000000E+0046, 1.4437500E+00, 1.4556000E+00, 0.0000000E+0047, 1.4437500E+00, 1.6011500E+00, 0.0000000E+0048, 1.4437500E+00, 1.4556667E-01, 0.0000000E+0049, 1.4437500E+00, 2.9113333E-01, 0.0000000E+0050, 1.4437500E+00, 4.3670000E-01, 0.0000000E+0051, 1.4437500E+00, 5.8226667E-01, 0.0000000E+0052, 1.4437500E+00, 7.2783333E-01, 0.0000000E+0053, 1.3100000E+00, 1.0189500E+00, 0.0000000E+0054, 1.3100000E+00, 1.1645000E+00, 0.0000000E+0055, 1.3100000E+00, 1.3100500E+00, 0.0000000E+0056, 1.3100000E+00, 1.4556000E+00, 0.0000000E+0057, 1.3100000E+00, 1.6011500E+00, 0.0000000E+0058, 1.3100000E+00, 1.4556667E-01, 0.0000000E+0059, 1.3100000E+00, 2.9113333E-01, 0.0000000E+0060, 1.3100000E+00, 4.3670000E-01, 0.0000000E+0061, 1.3100000E+00, 5.8226667E-01, 0.0000000E+0062, 1.3100000E+00, 7.2783333E-01, 0.0000000E+0063, 1.3100000E+00, 2.4744500E+00, 0.0000000E+0064, 1.3100000E+00, 2.3289000E+00, 0.0000000E+0065, 1.3100000E+00, 2.1833500E+00, 0.0000000E+0066, 1.3100000E+00, 2.0378000E+00, 0.0000000E+0067, 1.3100000E+00, 1.8922500E+00, 0.0000000E+0068, 1.1550000E+00, 1.8922500E+00, 0.0000000E+0069, 1.1550000E+00, 2.0378000E+00, 0.0000000E+0070, 1.1550000E+00, 2.1833500E+00, 0.0000000E+0071, 1.1550000E+00, 2.3289000E+00, 0.0000000E+0072, 1.1550000E+00, 2.4744500E+00, 0.0000000E+0073, 1.1550000E+00, 1.0189500E+00, 0.0000000E+0074, 1.1550000E+00, 1.1645000E+00, 0.0000000E+0075, 1.1550000E+00, 1.3100500E+00, 0.0000000E+0076, 1.1550000E+00, 1.4556000E+00, 0.0000000E+0077, 1.1550000E+00, 1.6011500E+00, 0.0000000E+0078, 1.1550000E+00, 1.4556667E-01, 0.0000000E+0079, 1.1550000E+00, 2.9113333E-01, 0.0000000E+0080, 1.1550000E+00, 4.3670000E-01, 0.0000000E+0081, 1.1550000E+00, 5.8226667E-01, 0.0000000E+0082, 1.1550000E+00, 7.2783333E-01, 0.0000000E+0083, 1.0000000E+00, 1.8922500E+00, 0.0000000E+0084, 1.0000000E+00, 2.0378000E+00, 0.0000000E+0085, 1.0000000E+00, 2.1833500E+00, 0.0000000E+0086, 1.0000000E+00, 2.3289000E+00, 0.0000000E+0087, 1.0000000E+00, 2.4744500E+00, 0.0000000E+0088, 1.0000000E+00, 1.0189500E+00, 0.0000000E+0089, 1.0000000E+00, 1.1645000E+00, 0.0000000E+0090, 1.0000000E+00, 1.3100500E+00, 0.0000000E+0091, 1.0000000E+00, 1.4556000E+00, 0.0000000E+0092, 1.0000000E+00, 1.6011500E+00, 0.0000000E+0093, 1.0000000E+00, 1.4556667E-01, 0.0000000E+0094, 1.0000000E+00, 2.9113333E-01, 0.0000000E+0095, 1.0000000E+00, 4.3670000E-01, 0.0000000E+0096, 1.0000000E+00, 5.8226667E-01, 0.0000000E+0097, 1.0000000E+00, 7.2783333E-01, 0.0000000E+0098, 1.1550000E+00, 2.2620000E+01, 0.0000000E+00100, 1.0000000E+00, 2.2620000E+01, 0.0000000E+00102, 1.1550000E+00, 2.2480140E+01, 0.0000000E+00103, 1.1550000E+00, 2.2340280E+01, 0.0000000E+00104, 1.1550000E+00, 2.2200420E+01, 0.0000000E+00105, 1.1550000E+00, 2.2060559E+01, 0.0000000E+00106, 1.1550000E+00, 2.1920699E+01, 0.0000000E+00107, 1.1550000E+00, 2.1780839E+01, 0.0000000E+00108, 1.1550000E+00, 2.1640979E+01, 0.0000000E+00109, 1.1550000E+00, 2.1501119E+01, 0.0000000E+00110, 1.1550000E+00, 2.1361259E+01, 0.0000000E+00111, 1.1550000E+00, 2.1221399E+01, 0.0000000E+00112, 1.1550000E+00, 2.1081538E+01, 0.0000000E+00113, 1.1550000E+00, 2.0941678E+01, 0.0000000E+00114, 1.1550000E+00, 2.0801818E+01, 0.0000000E+00115, 1.1550000E+00, 2.0661958E+01, 0.0000000E+00116, 1.1550000E+00, 2.0522098E+01, 0.0000000E+00

154

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155


156


157


158


159


160


161


162


163

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*ELEMENT, TYPE=CAX4 , ELSET=AXISYMMETRIC SOLID11, 2, 1, 27, 282, 32, 23, 3, 43, 31, 24, 23, 324, 30, 25, 24, 315, 29, 26, 25, 306, 28, 27, 26, 297, 28, 33, 6, 28, 4, 5, 37, 32

164

9, 29, 34, 33, 2810, 30, 35, 34, 2911, 31, 36, 35, 3012, 32, 37, 36, 3113, 5, 42, 43, 914, 38, 7, 8, 4715, 39, 38, 47, 4616, 40, 39, 46, 4517, 41, 40, 45, 4418, 42, 41, 44, 4319, 9, 52, 37, 520, 48, 10, 6, 3321, 49, 48, 33, 3422, 50, 49, 34, 3523, 51, 50, 35, 3624, 52, 51, 36, 3725, 47, 8, 11, 5726, 9, 43, 53, 1227, 43, 44, 54, 5328, 44, 45, 55, 5429, 45, 46, 56, 5530, 46, 47, 57, 5631, 12, 62, 52, 932, 58, 13, 10, 4833, 59, 58, 48, 4934, 60, 59, 49, 5035, 61, 60, 50, 5136, 62, 61, 51, 5237, 11, 67, 68, 1638, 63, 14, 15, 7239, 64, 63, 72, 7140, 65, 64, 71, 7041, 66, 65, 70, 6942, 67, 66, 69, 6843, 57, 11, 16, 7744, 12, 53, 73, 1745, 53, 54, 74, 7346, 54, 55, 75, 7447, 55, 56, 76, 7548, 56, 57, 77, 7649, 17, 82, 62, 1250, 78, 18, 13, 5851, 79, 78, 58, 5952, 80, 79, 59, 6053, 81, 80, 60, 6154, 82, 81, 61, 6255, 72, 15, 19, 8756, 16, 68, 83, 2057, 68, 69, 84, 8358, 69, 70, 85, 8459, 70, 71, 86, 8560, 71, 72, 87, 8661, 77, 16, 20, 9262, 17, 73, 88, 2163, 73, 74, 89, 8864, 74, 75, 90, 8965, 75, 76, 91, 9066, 76, 77, 92, 9167, 21, 97, 82, 1768, 93, 22, 18, 7869, 94, 93, 78, 7970, 95, 94, 79, 8071, 96, 95, 80, 8172, 97, 96, 81, 8273, 102, 98, 100, 38574, 15, 243, 244, 1975, 103, 102, 385, 38476, 104, 103, 384, 38377, 105, 104, 383, 38278, 106, 105, 382, 38179, 107, 106, 381, 380

165

80, 108, 107, 380, 37981, 109, 108, 379, 37882, 110, 109, 378, 37783, 111, 110, 377, 37684, 112, 111, 376, 37585, 113, 112, 375, 37486, 114, 113, 374, 37387, 115, 114, 373, 37288, 116, 115, 372, 37189, 117, 116, 371, 37090, 118, 117, 370, 36991, 119, 118, 369, 36892, 120, 119, 368, 36793, 121, 120, 367, 36694, 122, 121, 366, 36595, 123, 122, 365, 36496, 124, 123, 364, 36397, 125, 124, 363, 36298, 126, 125, 362, 36199, 127, 126, 361, 360100, 128, 127, 360, 359101, 129, 128, 359, 358102, 130, 129, 358, 357103, 131, 130, 357, 356104, 132, 131, 356, 355105, 133, 132, 355, 354106, 134, 133, 354, 353107, 135, 134, 353, 352108, 136, 135, 352, 351109, 137, 136, 351, 350110, 138, 137, 350, 349111, 139, 138, 349, 348112, 140, 139, 348, 347113, 141, 140, 347, 346114, 142, 141, 346, 345115, 143, 142, 345, 344116, 144, 143, 344, 343117, 145, 144, 343, 342118, 146, 145, 342, 341119, 147, 146, 341, 340120, 148, 147, 340, 339121, 149, 148, 339, 338122, 150, 149, 338, 337123, 151, 150, 337, 336124, 152, 151, 336, 335125, 153, 152, 335, 334126, 154, 153, 334, 333127, 155, 154, 333, 332128, 156, 155, 332, 331129, 157, 156, 331, 330130, 158, 157, 330, 329131, 159, 158, 329, 328132, 160, 159, 328, 327133, 161, 160, 327, 326134, 162, 161, 326, 325135, 163, 162, 325, 324136, 164, 163, 324, 323137, 165, 164, 323, 322138, 166, 165, 322, 321139, 167, 166, 321, 320140, 168, 167, 320, 319141, 169, 168, 319, 318142, 170, 169, 318, 317143, 171, 170, 317, 316144, 172, 171, 316, 315145, 173, 172, 315, 314146, 174, 173, 314, 313147, 175, 174, 313, 312148, 176, 175, 312, 311149, 177, 176, 311, 310150, 178, 177, 310, 309

166

151, 179, 178, 309, 308152, 180, 179, 308, 307153, 181, 180, 307, 306154, 182, 181, 306, 305155, 183, 182, 305, 304156, 184, 183, 304, 303157, 185, 184, 303, 302158, 186, 185, 302, 301159, 187, 186, 301, 300160, 188, 187, 300, 299161, 189, 188, 299, 298162, 190, 189, 298, 297163, 191, 190, 297, 296164, 192, 191, 296, 295165, 193, 192, 295, 294166, 194, 193, 294, 293167, 195, 194, 293, 292168, 196, 195, 292, 291169, 197, 196, 291, 290170, 198, 197, 290, 289171, 199, 198, 289, 288172, 200, 199, 288, 287173, 201, 200, 287, 286174, 202, 201, 286, 285175, 203, 202, 285, 284176, 204, 203, 284, 283177, 205, 204, 283, 282178, 206, 205, 282, 281179, 207, 206, 281, 280180, 208, 207, 280, 279181, 209, 208, 279, 278182, 210, 209, 278, 277183, 211, 210, 277, 276184, 212, 211, 276, 275185, 213, 212, 275, 274186, 214, 213, 274, 273187, 215, 214, 273, 272188, 216, 215, 272, 271189, 217, 216, 271, 270190, 218, 217, 270, 269191, 219, 218, 269, 268192, 220, 219, 268, 267193, 221, 220, 267, 266194, 222, 221, 266, 265195, 223, 222, 265, 264196, 224, 223, 264, 263197, 225, 224, 263, 262198, 226, 225, 262, 261199, 227, 226, 261, 260200, 228, 227, 260, 259201, 229, 228, 259, 258202, 230, 229, 258, 257203, 231, 230, 257, 256204, 232, 231, 256, 255205, 233, 232, 255, 254206, 234, 233, 254, 253207, 235, 234, 253, 252208, 236, 235, 252, 251209, 237, 236, 251, 250210, 238, 237, 250, 249211, 239, 238, 249, 248212, 240, 239, 248, 247213, 241, 240, 247, 246214, 242, 241, 246, 245215, 243, 242, 245, 244

*ELEMENT, TYPE=CAX4 , ELSET=AXISYMMETRIC SOLID1_1216, 390, 386, 532, 817217, 387, 531, 746, 675218, 817, 532, 388, 674219, 675, 746, 533, 389220, 391, 390, 817, 816

167

221, 392, 391, 816, 814222, 393, 392, 814, 815223, 394, 393, 815, 810224, 395, 394, 810, 812225, 396, 395, 812, 811226, 397, 396, 811, 813227, 398, 397, 813, 801228, 399, 398, 801, 805229, 400, 399, 805, 803230, 401, 400, 803, 804231, 402, 401, 804, 802232, 403, 402, 802, 807233, 404, 403, 807, 806234, 405, 404, 806, 808235, 406, 405, 808, 809236, 407, 406, 809, 783237, 408, 407, 783, 792238, 409, 408, 792, 791239, 410, 409, 791, 789240, 411, 410, 789, 790241, 412, 411, 790, 785242, 413, 412, 785, 787243, 414, 413, 787, 786244, 415, 414, 786, 788245, 416, 415, 788, 784246, 417, 416, 784, 796247, 418, 417, 796, 794248, 419, 418, 794, 795249, 420, 419, 795, 793250, 421, 420, 793, 798251, 422, 421, 798, 797252, 423, 422, 797, 799253, 424, 423, 799, 800254, 425, 424, 800, 747255, 426, 425, 747, 765256, 427, 426, 765, 764257, 428, 427, 764, 762258, 429, 428, 762, 763259, 430, 429, 763, 758260, 431, 430, 758, 760261, 432, 431, 760, 759262, 433, 432, 759, 761263, 434, 433, 761, 749264, 435, 434, 749, 753265, 436, 435, 753, 751266, 437, 436, 751, 752267, 438, 437, 752, 750268, 439, 438, 750, 755269, 440, 439, 755, 754270, 441, 440, 754, 756271, 442, 441, 756, 757272, 443, 442, 757, 748273, 444, 443, 748, 774274, 445, 444, 774, 773275, 446, 445, 773, 771276, 447, 446, 771, 772277, 448, 447, 772, 767278, 449, 448, 767, 769279, 450, 449, 769, 768280, 451, 450, 768, 770281, 452, 451, 770, 766282, 453, 452, 766, 778283, 454, 453, 778, 776284, 455, 454, 776, 777285, 456, 455, 777, 775286, 457, 456, 775, 780287, 458, 457, 780, 779288, 459, 458, 779, 781289, 460, 459, 781, 782290, 461, 460, 782, 676291, 462, 461, 676, 711

168

292, 463, 462, 711, 710293, 464, 463, 710, 708294, 465, 464, 708, 709295, 466, 465, 709, 704296, 467, 466, 704, 706297, 468, 467, 706, 705298, 469, 468, 705, 707299, 470, 469, 707, 695300, 471, 470, 695, 699301, 472, 471, 699, 697302, 473, 472, 697, 698303, 474, 473, 698, 696304, 475, 474, 696, 701305, 476, 475, 701, 700306, 477, 476, 700, 702307, 478, 477, 702, 703308, 479, 478, 703, 678309, 480, 479, 678, 686310, 481, 480, 686, 684311, 482, 481, 684, 685312, 483, 482, 685, 680313, 484, 483, 680, 682314, 485, 484, 682, 681315, 486, 485, 681, 683316, 487, 486, 683, 679317, 488, 487, 679, 690318, 489, 488, 690, 688319, 490, 489, 688, 689320, 491, 490, 689, 687321, 492, 491, 687, 692322, 493, 492, 692, 691323, 494, 493, 691, 693324, 495, 494, 693, 694325, 496, 495, 694, 677326, 497, 496, 677, 729327, 498, 497, 729, 728328, 499, 498, 728, 726329, 500, 499, 726, 727330, 501, 500, 727, 722331, 502, 501, 722, 724332, 503, 502, 724, 723333, 504, 503, 723, 725334, 505, 504, 725, 713335, 506, 505, 713, 717336, 507, 506, 717, 715337, 508, 507, 715, 716338, 509, 508, 716, 714339, 510, 509, 714, 719340, 511, 510, 719, 718341, 512, 511, 718, 720342, 513, 512, 720, 721343, 514, 513, 721, 712344, 515, 514, 712, 738345, 516, 515, 738, 737346, 517, 516, 737, 735347, 518, 517, 735, 736348, 519, 518, 736, 731349, 520, 519, 731, 733350, 521, 520, 733, 732351, 522, 521, 732, 734352, 523, 522, 734, 730353, 524, 523, 730, 742354, 525, 524, 742, 740355, 526, 525, 740, 741356, 527, 526, 741, 739357, 528, 527, 739, 744358, 529, 528, 744, 743359, 530, 529, 743, 745360, 531, 530, 745, 746361, 746, 745, 534, 533362, 745, 743, 535, 534

169

363, 743, 744, 536, 535364, 744, 739, 537, 536365, 739, 741, 538, 537366, 741, 740, 539, 538367, 740, 742, 540, 539368, 742, 730, 541, 540369, 730, 734, 542, 541370, 734, 732, 543, 542371, 732, 733, 544, 543372, 733, 731, 545, 544373, 731, 736, 546, 545374, 736, 735, 547, 546375, 735, 737, 548, 547376, 737, 738, 549, 548377, 738, 712, 550, 549378, 712, 721, 551, 550379, 721, 720, 552, 551380, 720, 718, 553, 552381, 718, 719, 554, 553382, 719, 714, 555, 554383, 714, 716, 556, 555384, 716, 715, 557, 556385, 715, 717, 558, 557386, 717, 713, 559, 558387, 713, 725, 560, 559388, 725, 723, 561, 560389, 723, 724, 562, 561390, 724, 722, 563, 562391, 722, 727, 564, 563392, 727, 726, 565, 564393, 726, 728, 566, 565394, 728, 729, 567, 566395, 729, 677, 568, 567396, 677, 694, 569, 568397, 694, 693, 570, 569398, 693, 691, 571, 570399, 691, 692, 572, 571400, 692, 687, 573, 572401, 687, 689, 574, 573402, 689, 688, 575, 574403, 688, 690, 576, 575404, 690, 679, 577, 576405, 679, 683, 578, 577406, 683, 681, 579, 578407, 681, 682, 580, 579408, 682, 680, 581, 580409, 680, 685, 582, 581410, 685, 684, 583, 582411, 684, 686, 584, 583412, 686, 678, 585, 584413, 678, 703, 586, 585414, 703, 702, 587, 586415, 702, 700, 588, 587416, 700, 701, 589, 588417, 701, 696, 590, 589418, 696, 698, 591, 590419, 698, 697, 592, 591420, 697, 699, 593, 592421, 699, 695, 594, 593422, 695, 707, 595, 594423, 707, 705, 596, 595424, 705, 706, 597, 596425, 706, 704, 598, 597426, 704, 709, 599, 598427, 709, 708, 600, 599428, 708, 710, 601, 600429, 710, 711, 602, 601430, 711, 676, 603, 602431, 676, 782, 604, 603432, 782, 781, 605, 604433, 781, 779, 606, 605

170

434, 779, 780, 607, 606435, 780, 775, 608, 607436, 775, 777, 609, 608437, 777, 776, 610, 609438, 776, 778, 611, 610439, 778, 766, 612, 611440, 766, 770, 613, 612441, 770, 768, 614, 613442, 768, 769, 615, 614443, 769, 767, 616, 615444, 767, 772, 617, 616445, 772, 771, 618, 617446, 771, 773, 619, 618447, 773, 774, 620, 619448, 774, 748, 621, 620449, 748, 757, 622, 621450, 757, 756, 623, 622451, 756, 754, 624, 623452, 754, 755, 625, 624453, 755, 750, 626, 625454, 750, 752, 627, 626455, 752, 751, 628, 627456, 751, 753, 629, 628457, 753, 749, 630, 629458, 749, 761, 631, 630459, 761, 759, 632, 631460, 759, 760, 633, 632461, 760, 758, 634, 633462, 758, 763, 635, 634463, 763, 762, 636, 635464, 762, 764, 637, 636465, 764, 765, 638, 637466, 765, 747, 639, 638467, 747, 800, 640, 639468, 800, 799, 641, 640469, 799, 797, 642, 641470, 797, 798, 643, 642471, 798, 793, 644, 643472, 793, 795, 645, 644473, 795, 794, 646, 645474, 794, 796, 647, 646475, 796, 784, 648, 647476, 784, 788, 649, 648477, 788, 786, 650, 649478, 786, 787, 651, 650479, 787, 785, 652, 651480, 785, 790, 653, 652481, 790, 789, 654, 653482, 789, 791, 655, 654483, 791, 792, 656, 655484, 792, 783, 657, 656485, 783, 809, 658, 657486, 809, 808, 659, 658487, 808, 806, 660, 659488, 806, 807, 661, 660489, 807, 802, 662, 661490, 802, 804, 663, 662491, 804, 803, 664, 663492, 803, 805, 665, 664493, 805, 801, 666, 665494, 801, 813, 667, 666495, 813, 811, 668, 667496, 811, 812, 669, 668497, 812, 810, 670, 669498, 810, 815, 671, 670499, 815, 814, 672, 671500, 814, 816, 673, 672501, 816, 817, 674, 673

*ELEMENT, TYPE=GAPUNI , ELSET=NODE TO NODE GAP2502, 98, 387503, 102, 531

171

504, 103, 530505, 104, 529506, 105, 528507, 106, 527508, 107, 526509, 108, 525510, 109, 524511, 110, 523512, 111, 522513, 112, 521514, 113, 520515, 114, 519516, 115, 518517, 116, 517518, 117, 516519, 118, 515520, 119, 514521, 120, 513522, 121, 512523, 122, 511524, 123, 510525, 124, 509526, 125, 508527, 126, 507528, 127, 506529, 128, 505530, 129, 504531, 130, 503532, 131, 502533, 132, 501534, 133, 500535, 134, 499536, 135, 498537, 136, 497538, 137, 496539, 138, 495540, 139, 494541, 140, 493542, 141, 492543, 142, 491544, 143, 490545, 144, 489546, 145, 488547, 146, 487548, 147, 486549, 148, 485550, 149, 484551, 150, 483552, 151, 482553, 152, 481554, 153, 480555, 154, 479556, 155, 478557, 156, 477558, 157, 476559, 158, 475560, 159, 474561, 160, 473562, 161, 472563, 162, 471564, 163, 470565, 164, 469566, 165, 468567, 166, 467568, 167, 466569, 168, 465570, 169, 464571, 170, 463572, 171, 462573, 172, 461574, 173, 460

172

575, 174, 459576, 175, 458577, 176, 457578, 177, 456579, 178, 455580, 179, 454581, 180, 453582, 181, 452583, 182, 451584, 183, 450585, 184, 449586, 185, 448587, 186, 447588, 187, 446589, 188, 445590, 189, 444591, 190, 443592, 191, 442593, 192, 441594, 193, 440595, 194, 439596, 195, 438597, 196, 437598, 197, 436599, 198, 435600, 199, 434601, 200, 433602, 201, 432603, 202, 431604, 203, 430605, 204, 429606, 205, 428607, 206, 427608, 207, 426609, 208, 425610, 209, 424611, 210, 423612, 211, 422613, 212, 421614, 213, 420615, 214, 419616, 215, 418617, 216, 417618, 217, 416619, 218, 415620, 219, 414621, 220, 413622, 221, 412623, 222, 411624, 223, 410625, 224, 409626, 225, 408627, 226, 407628, 227, 406629, 228, 405630, 229, 404631, 230, 403632, 231, 402633, 232, 401634, 233, 400635, 234, 399636, 235, 398637, 236, 397638, 237, 396639, 238, 395640, 239, 394641, 240, 393642, 241, 392643, 242, 391644, 243, 390645, 15, 386

173

************************MATERIALS*****************************SOLID SECTION,ELSET=AXISYMMETRIC SOLID1 ,MATERIAL=GENERIC_ISOTROPIC_STEEL*MATERIAL,NAME=GENERIC_ISOTROPIC_STEEL*ELASTIC,TYPE=ISOTROPIC2.99938E+07, 2.90000E-01*PLASTIC, HARDENING=ISOTROPIC52000,0.081000,0.28*SOLID SECTION,ELSET=AXISYMMETRIC SOLID1_1 ,MATERIAL=GENERIC_ORTHOTROPIC_STEEL*MATERIAL,NAME=GENERIC_ORTHOTROPIC_STEEL*ELASTIC,TYPE=ENGINEERING CONSTANTS1.6770E+06, 6.2288E+06, 1.46432E+07, 9.67E-02, 3.66E-02, 6.54E-02, 4.093E+05, 7.990E+051.6056E+06,****************************GAPS**************************************GAP, ELSET=NODE TO NODE GAP20.00000000E+00,

*FRICTION0.0000E+00,

**%*PHYSICAL CONSTANTS,STEFAN BOLTZMANN= 0.30840E-10,ABSOLUTE ZERO=-0.45967E+03**%****************************CONSTRAINT*********************************% CONSTRAINT SET 1*EQUATION

2,386, 1, 1.0, 15, 1, -1.0

2,386, 2, 1.0, 15, 2, -1.0

2,1, 2, 1.0, 22, 2, -1.0

2,2, 2, 1.0, 22, 2, -1.0

2,6, 2, 1.0, 22, 2, -1.0

2,10, 2, 1.0, 22, 2, -1.0

2,13, 2, 1.0, 22, 2, -1.0

2,18, 2, 1.0, 22, 2, -1.0

2,395, 1, 1.0, 238, 1, -1.0

2,395, 2, 1.0, 238, 2, -1.0

2,394, 1, 1.0, 239, 1, -1.0

2,394, 2, 1.0, 239, 2, -1.0

2,393, 1, 1.0, 240, 1, -1.0

2,393, 2, 1.0, 240, 2, -1.0

2,392, 1, 1.0, 241, 1, -1.0

2,392, 2, 1.0, 241, 2, -1.0

2,391, 1, 1.0, 242, 1, -1.0

2,391, 2, 1.0, 242, 2, -1.0

2,390, 1, 1.0, 243, 1, -1.0

2,390, 2, 1.0, 243, 2, -1.0

2,

174

14, 1, 1.0, 532, 1, -1.02,

14, 2, 1.0, 532, 2, -1.0**********************************************************************RESTART,WRITE*******************************LOADS**********************************AMPLITUDE,NAME=TEST.1 , 15000. , .2 , 17500. , .3 , 20000. , 1. , 22500.*AMPLITUDE,NAME=ZERO.1 , 22500. , 1.0 , 0.*AMPLITUDE,NAME=WORK.1 , 0.0 , 1. , 15000.*******************************TEST***********************************STEP,AMPLITUDE=RAMP,INC=10000TEST*STATIC**% BOUNDARY CONDITION SET 1**% RESTRAINT SET 1*BOUNDARY,OP=NEWBS000001, 2,, 0.00000E+00**% LOAD SET 1*DLOAD,AMPLITUDE=TESTBS000002, P1, 1.0000E+00BS000003, P3, 1.0000E+00*CLOAD,AMPLITUDE=TEST

22, 2,-3.1416E+00*NODE FILE,FREQUENCY= 1,GLOBAL=YESU,*EL FILE,FREQUENCY= 1,POSITION=NODES,DIRECTIONS=YESS,E*END STEP*******************************ZERO***********************************STEP,AMPLITUDE=RAMP,INC=10000ZERO*STATIC**% BOUNDARY CONDITION SET 1**% RESTRAINT SET 1*BOUNDARY,OP=NEWBS000001, 2,, 0.00000E+00**% LOAD SET 1*DLOAD,AMPLITUDE=ZEROBS000002, P1, 1.0000E+00BS000003, P3, 1.0000E+00*CLOAD,AMPLITUDE=ZERO

22, 2,-3.1416E+00*NODE FILE,FREQUENCY= 1,GLOBAL=YESU,*EL FILE,FREQUENCY= 1,POSITION=NODES,DIRECTIONS=YESS,E*END STEP*******************************WORK***********************************STEP,AMPLITUDE=RAMP,INC=10000WORK*STATIC**% BOUNDARY CONDITION SET 1**% RESTRAINT SET 1*BOUNDARY,OP=NEWBS000001, 2,, 0.00000E+00**% LOAD SET 1*DLOAD,AMPLITUDE=WORKBS000002, P1, 1.0000E+00BS000003, P3, 1.0000E+00*CLOAD,AMPLITUDE=WORK

22, 2,-3.1416E+00*NODE FILE,FREQUENCY= 1,GLOBAL=YESU,*EL FILE,FREQUENCY= 1,POSITION=NODES,DIRECTIONS=YESS,E*END STEP********************************************************************************NSET,NSET=BS000001

175

98,100,387,389,675*ELSET,ELSET=BS00000267,68,69,70,71,72*ELSET,ELSET=BS00000355,56,57,58,59,60,61,62,63,64,65,66,73,74,75,7677,78,79,80,81,82,83,84,85,86,87,88,89,90,91,9293,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204205,206,207,208,209,210,211,212,213,214,215

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